'They Loved to Laugh' by Katheryn Worth appears to have all the features mentioned.
16-year-old orphan Martitia Howland has been transplanted into a Quaker farm family of five intimidating sons and one disapproving daughter. As Martitia runs their gauntlet, she suffers their teasing but finally begins to bloom. Valiantly she acquires the skills they expect of her, and discovers other gifts all her own. Her achievements earn respect in the end and more, her heart's true love.
Also on Amazon, reviewer eldeberryjam comments:
The main character in this book - the orphan - takes over the family silk production and weaving because the daughter who had learned this job had married and left home. There is a significant Quaker historical element to this story. Silk was a "free labor" fiber, an alternative to cotton, prior to the Civil War. Quakers were admonished by their meetings if they kept slaves, so they usually attempted to do all of their own labor. Many raised and processed their own fibers - wool from sheep, linen from flax, and silk from moth larvae eating mulberry leaves. This young woman learned how to raise, process and weave silk in North Carolina.