Strange issue I've just noticed. The "approx total memory" for my GPU, reported by dxdiag says 3825MB, but I have a Sapphire HD6950 2gb (reference model). Even stranger, I just bought a new 2gb RAM module to upgrade me from 4 - 6gb DDR2-800, and when I installed it, dxdiag now reports 751MB. With, or without the RAM, Sapphire TRIXX correctly reports 2048MB.
My guess is that dxdiag is reporting incorrectly for some reason, but I'd like to make sure this isn't limiting GPU performance somehow.
DXDiag tends not to report graphics RAM properly, this is a common issue. If you are concerned about not getting the performance you should, you can always run some benchmarks in some of your games and compare them against the results that hardware review sites have. Only be concerned if you aren't getting the performance that the card should be offering.