Scubakevdm:..
In contrast, being underweighted generally prevents the diver from leaving the surface in the first place. I understand that the air in the diver's tank has weight, and that it's conceivable that they would be able to descend at the beginning of the dive, however, for a single 80 foot tank, you're looking at about a five pound swing between full and empty, so no matter what, if they descend they're less than 5lbs underweighted. Furthermore, in this scenario, they would have no air in their BCD, and the extra weight of the air is lost gradually, and so they gradually drift upwards to the surface.
One could argue that the diver could swim down and maintain depth with propulsion, and though certainly this is somewhat risky, the fact of the matter is that most divers will not do this, or get tired of doing it very quickly, or burn through their tank quickly. In any event it certainly limits the time spent at depth.
I was more thinking of being under weighted in the sense of being able to make a controlled ascent. Gas and Buoyancy swing are over weighted easily, but I would rather be overweighted by 5 pounds than underweighted by that amount not being able to hold depth. But this now seems to go outside of the original question. The point I was making is that many professional focus on over weighting, rather than also looking at the flipside of that coin.