I prefer 28" barrels on all gauges. Weights: 20's right around 6 lbs., 16's at about 6-1/2lbs, 12's at 7 lbs. or a bit more - light enough to carry but with enough weight to feel the swing and take a bit of recoil off my shoulder.
The guns I shoot most often (all 16's/28") are a Fox A Grade at 6-4, a Fox Sterlingworth at 6-8 and a Parker Trojan at 6-9. I have some 20's and 12's but frankly I rarely shoot them.
Weight has never been my first question about a gun; it's all about the feel. I do get a kick out of guys that are 20+lbs. overweight obsessing about a couple ounces on a shotgun
.