I think you're confusing "Heavy" with "Sluggish"
Heavy: Flies less when hit, does more damage when attacking, jump height may or may not be as high as others.
Charizard is definitely heavy. In the games the three 3rd Forms of the starters were some of the heaviest (One of the many things PokeDex tells you is weight) in the game, the heaviest being Venusaur (i think), surpassed only by Onix, Snorlax, and Mewtwo...
Sluggish: Not agile. Attacks slowly, etc...
Ike is Sluggish, but, if I'm to believe what I've heard, he's not all that Heavy.
Prime examples of characters who is Heavy but not Sluggish (not a smasher), would probably be T-Hawk and Sagat from Street Fighter, though it's not the same thing...
Since Sluggishness and Heaviness usually go hand in hand in fighting games, especially in the Smash games, I can see where you're coming from (which is why the heavy smashers tend to have somewhat bad reputations), but remember that Brawl is a new game, with most things being optimized, so it may not be necessarily so.