I see this pop up quite regularly on RPG forums, and it isn't even a debate. Why do so many people think weapons weigh(ed) so much? Because games are primarily made and played by people who 1) are relatively weak, 2) have never tried to swing around something weighing 5-10lbs+ for any length of time, or 3) both.
I haven't done any fighting with medieval weapons, but I regularly split wood using a woodsplitting maul; weight: 8lbs. I'm stronger and fitter than the average guy, and while I can work with it fairly comfortably for an hour or two, I wouldn't want to fight with it for long, and if you asked me to wield it in one hand I'd laugh at you.
All the sources are there; weapons made for war weren't very heavy at all. Remember, in the real world, the people fighting, and designing weapons for fighting, were being as practical and as effective as they possibly could be. They weren't trying to look good, or impress anyone, or try a different style; they were just trying not to die, and I can bet the vast majority of those men wished they were somewhere else. Fearless, bloodsoaked heroic warriors in history are about as realistic as 30lb weapons.
As for how strong people were back then... I dunno. I'm not a historian of any kind, but I do know that modern people (at least here in the opulent west) are, on average, in absolutely horrible physical condition, and eat crap they call "food." I'm 5'7", and I bet I'm much stronger than the average 6' guy who doesn't train; I'd give the small, malnourished soldier of history the benefit of the doubt over the tall, unconditioned office worker of today, any day.
tl;dr- the OP is correct. If you doubt him, pick up something that weighs 10lb+ and swing it around for 15 minutes. Don't hurt yourselves.