Moreover if you want to talk spinning — I'm actually more of a spinner than a weaver because I spend a lot of time knitting my output. I use a spinning wheel. The spinning wheel was a technology that increased the efficiency of spinning a fiber into thread by more than an order of magnitude. I can spin with a spindle, and for very specific technical tasks it's preferable.
eg: spinning very delicate threads is easier on a drop spindle than on a spinning wheel.
Now, on how the rhythms of spinning and weaving fit into agricultural life around the Iron Age and after, into the pre-industrial revolution: making yardage was a family affair. The retting and shearing could be done by anyone. Carding and combing were simple tasks that you could delegate to children. After that, the women and older girls would spin the thread. Spinning was often saved for a winter task — you didn't need much light to do it competently.
Weaving, on the other hand, was a summer task — the kind of thing you could use the long daylight hours to do. This is because if you slip up in your weaving you can threaten the entire structural integrity of the cloth.
Moreover, what people value in weaving and spinning then and now is completely different. Back before the industrial production of cloth, girls and women were trained extensively to turn out fine, delicate handspuns. I have seen a delicate piece of linen cloth dated to the antebellum era of the US that was translucent, woven as a sampler to show off a young lady's skills. Consistency and regularity were vital.
Such consistency and delicacy was heavily devalued with factories turning out stuff, so nowadays consumers prefer handwovens and handspuns that reflect a slight human irregularity in the touch, or a method of spinning and plying that machines cannot replicate.
So back in the era of UnReal World, a young woman who could spin fine thread and weave fine cloth would be considered extremely marriageable, because if she was swift and efficient at it, and also knew how to dye cloth appealing colors, she could put some of her spare cloth on the market because it was ULTRA-VALUABLE.
As for historical dye plants: people used all kinds of dyeherbs. Woad for blue, onion skins or dyers' chamomile (Anthemis tinctoria) for yellow, madder root for red. Note that this is a very, very short list. Most of these natural dyes require a mordant, or a metal salt, to make sure the colors chemically bond to the fabric. Some of the mordants used are pretty harmless — alum, for example, is used to mordant some colors, but too much of it will leave wool and other protein fibers with a weird sticky texture. Other mordants are shit you need chemical disposal facilities to get rid of.
As a contemporary fiber crafter, I use acid dyes, which bond to protein fibers effortlessly with the addition of citric acid or vinegar.
A large amount of the colonization of Mexico by the Spanish was driven by a consumer craze for lightfast intense red dye, which was derived from the cochineal insect that fed on prickly pear cacti. Similarly, both indigo and cotton drove chattel slavery to a great extent (although not as great as the consumer desire for sugar.)
(I know most of this stuff because my university education is on theatrical costume production — but I was already spinning and weaving before I became a costume technician, and my gateway craft was knitting.)