Basically they should be getting 1/4 to 1/3 cup of pellets per 5 pounds of body weight. That’s from my vet. It’s really important not to overfeed pellets, because they’re the things that will make your bunny gain weight quickly.

Here’s the rest, from my vet (she’s absolutely phenomenal):
Babies: Birth to 3 wks: mother’s milk
3-7 wks: mother’s milk, alfalfa and pellets
7 wks to 7 months: unlimited pellets, unlimited hay
12 weeks: introduce vegetables (one at a time, quantities under 1/2 oz)

Young Adults (7 months to one year)
-introduce timothy hay, grass hay, and oat hays, decrease alfalfa
-decrease pellets to 1/2 cup per 6 lbs body weight
-increase daily vegetables gradually
-fruit daily ration no more than 1 oz to 2 oz per 6 lbs body weight

Mature Adults (1 to 5 years)
-unlimited timothy, grass hay, oat hay, straw
-1/4 to 1/2 cup pellets per 6 lbs body weight
-minimum 2 cups chopped vegetables per 6 lbs body weight
-fruit daily ration no more than 2 oz per 6 lbs body weight

Senior Rabbits (over 6 yrs)
-if sufficient weight is maintained, continue adult diet
-frail, older rabbits may need unrestricted pellets to keep weight up
-alfalfa can be given to underweight rabbits, only if calcium levels are normal
-annual blood workups are highly recommended for geriatric rabbits

Size does make a difference in the quantity of food. First, re the little one – I would use only Timothy-based adult pellets (most of us use Oxbow as a healthy brand but you can find others) so the fat content is on the lower side. (No additives like the colorful ones they sell at pet stores. Those are like tossing in cookies.) No alfalfa in pellets or hay.
Keep him on lots of fresh hay and water to keep his digestion moving and help him stay slim. You want him to eat more hay, less greens, and even less pellets so 1/4 cup a day max. of pellets is enough, possibly less for a smaller bunny. If he finishes them, don’t replenish until the next day. But if he finishes his hay, replenish all he wants.

Veggies for an 8lb. rabbit is about a cup twice a day, or your basic handful. NOT mashed down, but fluffy. I give a handful of romaine and Kale for example, and if it falls out of my hand, it’s too much.
Fruits are not necessary daily – they are treats. Limit them, though a fruit treat once a day is OK. Carrots are more like fruits, so I only use baby carrots, 2 daily at the most, or cut carrots the same size or smaller. Banana slices about 1/4 inch thick max. Only a couple times a week at the most. Raisins are better as a treat because 2 or 3 every couple of days is fine. Apple chunks, also about the size of the banana pieces. One grape. One or the other, not combined. Some greens, like mint or dill, can also be used as treats. Just think of fruits as all sugar.

If your bunnies have unlimited hay, handfuls of greens 2x daily and small amounts of pellets as their regular diet, they will be happy but not fat.

A 2 month old rabbit shouldn’t be overweight. Recommendations are for unlimited pellets and they grow very very fast at this age, so the chance of being overweight is unlikely. Have to taken a stool sample to the vet? The round belly might be an indication of a parasite.

At that age, I’m also questioning if it may be a parasite. Has she had a fecal exam?

Rabbits generally get parasites from other rabbits that are infected. Since she is so young, she must have been with her mother fairly recently and could have picked one up from her.