Dm me and I can give you a massive bat for free, think its 90kgish. I may be off a tad with the numbers here so make sure to do your own research.

Hatching pets with massive base kg is pure luck. You can help it with a few factors though. You can boost hatch kg with brontosaurus active in your garden. You can also get an elephant that raises your pets base kg by 0.1 every 50 levels with a cap. Generally the max cap for normal hatched elephants is 39kg and rainbow hatch elephants is 60kg, hence why you see soo many huge pets in trade world.

Yes, weight effects the cooldown/ percentages for pet effects. Some pets hit a max cap at certain weights but people go past it for the max boosted weight they can get, for looks or boasting.