According to this XGN report, a chap's been told by Wii Fit that he's heavy to play the game.
"Well yesterday was a bummer for me," said the unnamed gamer. "I finally got a chance to step on the balance board to play Wii Fit. As soon as I was beginning the process creating profile, it said that I exceeded the board's 330 lbs weight limit and cancelled the registration. At 6'8'', I'm not terribly overweight and it's not that hard for someone that size to weight that much."
The man in question weighs 350 lbs, apparently.
Wii Fit appears to be good at telling people they're too big. Still no report of someone being told they're too thin yet. The year's still young, though.