That'd make the heavy characters completely useless, once you're behind, there's no way to catch up anymore!
Yes, except for items and doing better in the pack.
Heavy characters in Mario 64 have tighter handling than lighter characters and can cause them to spin out when bumping into them.
How, if both your acceleration and your top speed is worse?
I'm not sure what exactly "how" is referring to, but by "tight handling" I mean having a smaller turning radius and losing less speed when turning.
It's not a big difference and you can't be at top speed for long.
It was similar in the original Mario Kart of the SNES. I clearly remember always choosing toad or koopa because they "felt" the more average to me. Donkey Kong was difficult to handle and also had slow acceleration, same with bowser.