I think if it's overweight you just get the weight down like before.
If they eat too much Icecream they get the toothache symbol.
If they play in the rain I really don't think it's a big deal they won't get sick.
I think it's just like before they'll get sick if left unfed for too long and if too much poo is left on screen. Also they will change colors if you don't bathe your Tamagotchi character everynight.