The Reign of Josiah in Judah, the Southern Kingdom
Approximately 639-609 BCE
Context: This story takes place after Assyria's conquest of most of Judah in 701 BCE, shortly before the Babylonian conquest and destruction of the First Temple in 598/7 BCE (Efron, Lehman, and Weitzman, "Timeline of Jewish History,” The Jews: A History, 519).
Historicity: This is not a historical source, but a reflection of the author's perspective: the destruction of the Temple was punishment by G-d for their worship of other Gods. It's attributed to the first Deuteronomistic historians--people who were influenced by Deuteronomic writings (Zevit,"Introduction to Kings," The Jewish Study Bible, 653-5).

(יא) וַֽיְהִי֙ כִּשְׁמֹ֣עַ הַמֶּ֔לֶךְ אֶת־דִּבְרֵ֖י סֵ֣פֶר הַתּוֹרָ֑ה וַיִּקְרַ֖ע אֶת־בְּגָדָֽיו׃
(11) When the king heard the words of the scroll of the Teaching, he rent his clothes.
...
(14) So the priest Hilkiah, and Ahikam, Achbor, Shaphan, and Asaiah went to the prophetess Huldah—the wife of Shallum son of Tikvah son of Harhas, the keeper of the wardrobe—who was living in Jerusalem in the Mishneh, and they spoke to her.
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(17) Because they have forsaken Me and have made offerings to other gods and provoked My anger with all their deeds, My wrath is kindled against this place and it shall not be quenched.
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[King Josiah] brought out the [image of] Asherah from the House of the LORD to the Kidron Valley outside Jerusalem, and burned it in the Kidron Valley; he beat it to dust and scattered its dust over the burial ground of the common people.
וַיִּתֹּץ֙ אֶת־בָּתֵּ֣י הַקְּדֵשִׁ֔ים אֲשֶׁ֖ר בְּבֵ֣ית יְהֹוָ֑ה אֲשֶׁ֣ר הַנָּשִׁ֗ים אֹרְג֥וֹת שָׁ֛ם בָּתִּ֖ים* לָאֲשֵׁרָֽה׃
He tore down the cubicles of the male prostitutes in the House of the LORD, at the place where the women wove coverings* for Asherah.
*The meaning of this word is debated.
Spindle
Spindle; Akhzib; Iron Age II, 8th-6th century BCE; Bone; L: 6.7; Diam: 3 cm; Israel Antiquities Authority; IAA: 1948-491
Apocalypse of II Baruch (Syriac) - Translated Text Unavailable*
Approximately early 100s CE
*=Relevant parts are paraphrased based on summaries by Miriam Peskowitz, Spinning Fantasies. Summaries are also available online by Crawford Howell Toy and Louis Ginzberg through the Jewish Encyclopedia.
Context: II Baruch, written in the early 2nd century, is a one of the only available non-rabbinic writings from this period. It is an apocalyptic text that was likely originally written in Hebrew, which was then translated into Greek and finally into Syriac––the only existing language of the text today. This text was transmitted by Christian scribes (Peskowitz, 1997, Spinning Fantasies, 160). It's unclear from where this text originated.
Summary of Text
The story of II Baruch takes place in the time of the destruction of the First Temple. He mourns the Temple and curses the priests. While despairing in the ruins of the Temple, Baruch witnesses an angel visit the Holy of Holies. The angel removes a number of items, including the woven veil that divided the Holy of Holies from the rest of the Temple. The angel then buries the items deep in the earth and tells other angels to destroy Jerusalem. After God’s presence leaves the temple, people of the city leaves–but God tells Baruch to stay. (ibid., 161).
Baruch then instructs spinners––virgin women––to offer burn their linens and tools as if they're holy objects. Peskowitz writes,
“[I]n the female bodies of virgin spinners, Baruch finds an image of redemption for Jews. In the lament’s final verse, Baruch uses the virgin spinners to express his hopes for purity, possibility and the future. The spinners emulate the priests, in a way....the spinners throw their tools to the fire: ‘And you, virgins who spin linen, and silk with the gold of Ophir: make haste and take all things and cast them into the fire so that it may carry them to him who made them’
“In the lament, the virgins are spinning luxury thread. Metaphorically, gold from Ophir is the highest quality gold, procured by Solomon for the Temple and worn as luxury ornaments by women in the royal court.” (ibid. 161-2)
"The Cave of the letters, used as a refuge place by Jewish rebels at the end of the Bar Kokhba revolt, yielded a variety of personal effects that the women of the company had taken with them into hiding: wool, spindles and thread, jewelry and jewelry boxes, sandals and other clothing items, mirrors, and fine housewares. This is a unique collection of finds, which survived the ravages of time thanks to the dry climate of the desert, providing an invaluable glimpse into daily life in the Roman Period."
Cave of the Letters Judean Desert; Roman period, 132-135 CE; Iron, wood, wicker, twigs and asphalt, copper and tin; Israel Antiquities Authority; IAA: 1996-292, 1996-9114, 1996-307, 1996-305, 1996-9113, 1996-9112, 1996-9111, 1961-1364, 1996-301. Photo © Israel Museum, Jerusalem, by Moshe Caine, https://www.imj.org.il/en/collections/395651-0.
Masechet Ketubot ("Marriage Contracts") Seder Nashim ("Order of Women"), Mishnah
Canonized in 220 CE, began composition in 63 CE
Context: The Second Temple has fallen and Jews are attempting to reconstruct their lives and practices. The Mishnah is understood to record Pharisees' oral tradition, as remembered by Judah Ha-Nasi, the Patriarch. The text was likely written somewhere north of Jerusalem in Sephoris, a Galilean city (Efron, Lehman, and Weitzman, "Timeline of Jewish History,” The Jews: A History, 136-7).

(ה) אֵלּוּ מְלָאכוֹת שֶׁהָאִשָּׁה עוֹשָׂה לְבַעְלָהּ, טוֹחֶנֶת, וְאוֹפָה, וּמְכַבֶּסֶת, מְבַשֶּׁלֶת, וּמֵנִיקָה אֶת בְּנָהּ, מַצַּעַת לוֹ הַמִּטָּה, וְעוֹשָׂה בַצֶּמֶר. הִכְנִיסָה לוֹ שִׁפְחָה אַחַת, לֹא טוֹחֶנֶת, וְלֹא אוֹפָה וְלֹא מְכַבֶּסֶת. שְׁתַּיִם, אֵינָהּ מְבַשֶּׁלֶת וְאֵינָהּ מֵנִיקָה אֶת בְּנָהּ. שָׁלֹשׁ, אֵינָהּ מַצַּעַת לוֹ הַמִּטָּה וְאֵינָהּ עוֹשָׂה בַצֶּמֶר. אַרְבָּעָה, יוֹשֶׁבֶת בַּקַּתֶּדְרָא. רַבִּי אֱלִיעֶזֶר אוֹמֵר, אֲפִלּוּ הִכְנִיסָה לוֹ מֵאָה שְׁפָחוֹת, כּוֹפָהּ לַעֲשׂוֹת בַּצֶּמֶר, שֶׁהַבַּטָּלָה מְבִיאָה לִידֵי זִמָּה. רַבָּן שִׁמְעוֹן בֶּן גַּמְלִיאֵל אוֹמֵר, אַף הַמַּדִּיר אֶת אִשְׁתּוֹ מִלַּעֲשׂוֹת מְלָאכָה, יוֹצִיא וְיִתֵּן כְּתֻבָּתָהּ, שֶׁהַבַּטָּלָה מְבִיאָה לִידֵי שִׁעֲמוּם:
(5) And these are tasks that a wife must perform for her husband: She grinds wheat into flour, and bakes, and washes clothes, cooks, and nurses her child, makes her husband’s bed, and makes thread from wool by spinning it. If she brought him one maidservant, i.e., brought the maidservant with her into the marriage, the maidservant will perform some of these tasks. Consequently, the wife does not need to grind, and does not need to bake, and does not need to wash clothes. If she brought him two maidservants, she does not need to cook and does not need to nurse her child if she does not want to, but instead may give the child to a wet nurse. If she brought him three maidservants, she does not need to make his bed and does not need to make thread from wool. If she brought him four maidservants, she may sit in a chair [katedra] like a queen and not do anything, as her maidservants do all of her work for her. Rabbi Eliezer says: Even if she brought him a hundred maidservants, he can compel her to make thread from wool, since idleness leads to licentiousness. Consequently, it is better for a woman to be doing some kind of work. Rabban Shimon ben Gamliel says: Even one who vows that his wife is prohibited from doing any work must divorce her and give her the payment for her marriage contract, since idleness leads to idiocy.
And these are examples of women who may be divorced without payment of their marriage contract: A woman who violates the precepts of Moses, i.e., halakha, or the precepts of Jewish women, i.e., custom. The Mishna explains: And who is categorized as a woman who violates the precepts of Moses? This includes cases such as when she feeds him food that has not been tithed, or she engages in sexual intercourse with him while she has the legal status of a menstruating woman, or she does not separate a portion of dough to be given to a priest [ḥalla], or she vows and does not fulfill her vows. And who is considered a woman who violates the precepts of Jewish women? One who, for example, goes out of her house, and her head, i.e., her hair, is uncovered; or she spins wool in the public marketplace; or she speaks with every man she encounters. Abba Shaul says: Also one who curses his, i.e., her husband’s, parents in his presence. Rabbi Tarfon says: Also a loud woman. And who is defined as a loud woman? When she speaks inside her house and her neighbors hear her voice.

Bonus!
Terminology and methods for weaving and spinning is featured in the Tanach.