Welcome, Barley!
Many weeds have deeper roots or evaporate water more slowly than typical lawn grasses. The grass' defense against drought is to drop its above ground parts, so the roots survive. The weed's defense is to grow its roots even deeper, grow its top more slowly--often with narrower leaves, which evaporate water even more slowly--and maybe go to seed early.

Yes, welcome Barley. Even very large woody bamboo's (still grasses) have horizontal rhizomes that don't go deep at all, just a couple of feet. They live in well watered areas so don't have a problem though this shallow rhizome/rooting is common to all the grass family as Tugbrethil has said. Everything goes to the roots in a drought (apart from the one and only leaf succulent in the entire family, Dregeochloa pumila). I want this plant!

Agree with the above for perennial weeds, but also would say this is the phenomenon commonly known as sod's law - another example is when you sow grass seed and it comes up patchy in the lawn area, and grows like billy oh in the border where you didn't even put it. "Weeds" are opportunistic, the seeds are sitting in the soil just waiting for a bit of moisture - as soon as it arrives,up they come - a lot of them have a brief life anyway, depending on what they are.