The dude has strips of metal grafted to the major bones of his body; that's got to add some weight. The adamantium grafted on to Wolverine's skeleton is often described as "unbreakable," but I've never seen it described as "incredibly light." Wolverine's strong - anyone would be if they had to lug all that extra metal around. Mr. T, for instance. But is Wolverine strong enough to actually... swim?
Nay! He'd sink like a stone.
If I were on the Hellfire Club or something, the next time Wolverine attacked our mansion I would just throw a few donuts and a six-pack of Labatt's into the deep end of the Olympic-size pool in the basement and call it good.