Should I use lighter or heavier paper for my printed dissertation? My university requires one to submit a printed copy of the dissertation. The paper has to be 100% cotton, white, and 20- to 24 lb weight.

Since I have a choice in the weight of the paper, my question is if there are any advantages to one weight over the other.
I don't think the weight of the paper is as important as the material from which it is made. So long as the paper is "archival quality," meaning no acids or other components which will allow it to degrade more easily over time, the choice is somewhat arbitrary. Willie Wong raises some valid points in his answer, though—the slightly thicker paper will help future readers more than the thinner paper, and the relative change in weight is probably not so large as to make the thesis cumbersome as a printed volume.