Neither of mine had weight issues after being fed unlimited pellets as babies. When I say unlimited, I mean as much as they’ll eat in a reasonable amount of time. If a bunny is a little piggy and gobbles up all of the pellets no matter how many you give them, then I would say there is a problem.
For smaller breeds, it is recommended that their pellets are cut back after they are 6 months old. Larger breeds can have unlimited pellets longer since they continue to grow after 6 months of age.
As far as developing problems later on goes, I’m assuming you mean they become addicted to pellets. While my boys love their pellets, I wouldn’t say they are addicted to them. Some people feed them based on body weight. Others feed them as treats or in very small amounts or none at all. Feeding no pellets at all can be difficult because it’s hard to ensure they are getting everything they need from the veggies they get. You have to provide a wide variety and bunny has to actually want to eat that wide variety.
I don’t know what brand of pellets you’re feeding. I use Oxbow and it says 1/8 cup daily for 1-4lbs (for the adult formula). For the young bunny formula, they advise feeding unlimited pellets.