Still thinking the stats don't matter.
Perhaps a rework?
Middleweights have no spectacular stats, but they could be the show-offs and are excellent with drifts (and drift boosts) and stunts. This is to allow them to fulfill a niche that actually makes middleweights more viable and not left out over the tussle between lights (where they dominate in Mario Kart 64 and Super Circuit) and heavies (where they dominate in pretty much everything else).
Lightweights can be speedy with good acceleration to boot, but they get bad items and get knocked around a lot.
Heavyweights have the best control and get the best items, but they're pretty slow. They can ram other racers and cause them to lose control, lose items, whatever fits better and doesn't make them broken.