You've likely worn knit socks and T-shirts -- they're machine-knit. A lot of clothing is knit, not woven. Fabric does not have to use big and chunky threads to be knit; the loops can be quite a small gauge in size.

I don't think I've ever seen socks or T-shirts that weren't (machine) knitted. Knitting produces more stretchy fabric than weaving so it's better for garments that fit closely.