You are right about wet carpet being pretty heavy. We have learned to look for short nap and thin carpet when we need to replace the carpet which isn't very often. We pass on heavy plush carpets.
We can also be a bit inattentive on weeding. We haven't had much trouble with weeds on the carpets. We left one out over winter one year and they grew pretty good on top of the one carpet but they pulled right up without any trouble. Now we always roll them up at the end of fall and set them along side the edge of the garden.