Definitely limit the greens. I wouldn't recommend over 1-2 leaves a day. The only green I prefer to give my rabbits is Comfrey. I'll give them about 1/2 leaf to 1 leaf per day. With a small rabbit like yours, which looks like a Netherland Dwarf cross, I wouldn't feed over 1 leaf a day at most. Otherwise you are going to risk your rabbit getting diarrhea.
Rabbits love to eat greens, but just because they love to eat them doesn't mean they are good for them.
As far as the amount you should feed your rabbit, the easiest and best method is to watch how much it eats. Feed the pellets before feeding any greens. You don't want your rabbit to fill up on greens then not eat it's pellets. That's like giving a kid candy and sweets before dinner. They fill up on sweets then don't have room for the meal that has the nutrition they really need.
When you feed your rabbit pellets give it just what it will eat in 24 hours. If it doesn't eat it all, reduce the amount you give it by the amount left in the bowl or feeder. Your rabbit should just barely clean up the bowl in 24 hours.
Normally, rabbit breeders refer to the amount of feed they feed their rabbits in two ways (ounces and cups). A 1 cup cooking measuring cup holds about 6 ounces of rabbit pellets. You can weigh them on a dietary scale if you're curious to see if I'm right. I raise New Zealands which are a bigger breed of rabbit. They eat about 6 ounces or 1 cup of feed a day. A rabbit about the size of yours will eat about 3-4 ounces of feed a day or about a 1/2 cup to a 2/3 cup of feed.
Keep in mind that those weights are if you feed nothing but pellets. If you give your rabbit say 2 ounces of greens, it is only going to want to eat 2 ounces of pellets most likely. Never make greens, fruits, or vegetables over one quarter of the rabbit's diet.
Be very wary of people that tell you to feed your rabbits greens and vegetables and tell you how good they are for your rabbit. Many of them don't have much experience raising rabbits. Even many veterinarians know very little about rabbit medicine or rabbit diets. Most veterinarians are only familiar with dogs and cats.
I studied animal nutrition in college at Purdue University and I've read several books and articles on rabbit nutrition. There are good sources out there some are:
1. The American Rabbit Breeders Association - they have been around for almost 100 years and work with a number of universities on rabbit research concerning rabbit nutrition and rabbit diseases
2. Peter R. Cheeke - an auther of a couple books on rabbits and rabbit nutrition. He is probably one of he foremost authorities on rabbit nutrition. He is a professor at Oregon State University and does research on rabbit nutrition. You'll find that many of the articles on rabbit nutrition reference his name and his work.
3. Dr Terry E Reed - A former president of the ARBA, rabbit veterinarian, and the person who formulated Heinold Feeds. He's written several articles on rabbit nutrition and rabbit diseases and was valedictorian of his veterinarian class at Purdue University.
4. Dr Chris Hayhow - Current president of the ARBA. He's also a rabbit veterinarian and he specializes in microbial research and animal diseases. He's very knowledgable about rabbit diseases.
There are reasons why vegetables and greens are bad for a rabbit. Anyone that knows how a rabbit's digestive system works and the traits of vegetables and greens should know why they are disagreeable with rabbits.
Here are some reasons why:
1. Low in protein - rabbits need protein to grow properly
2. Low in fiber - fiber helps prevent diarrhea
3. High in energy - a high energy diet will make a rabbit fat and will make it molt more
4. High in water - cause retention of water which can lead to GI Stasis or diarrhea
Fiber means that the food contains bigger less digestible pieces in the food. Those pieces get separated in the intestinal tract of the rabbit after the colon and exit the rabbit quicker. Smaller partices (food with less fiber) and water get routed back to the colon. This is part of the rabbit's digestive system to help it retain water and nutrients. However, in this case it back fires with greens. Since greens are low in fiber and high in water content, they hold them in their body longer and they flow back to the colon. The longer they stay in the colon, the longer bacteria builds up in the colon. When the bacteria builds up to a certain level it gives the rabbit diarrhea (bacterial enteritis). Also, since the rabbit retains the food longer it raises the risk of the gastro intestinal tract stopping up (GI stasis) since the food isn't moving as quickly through. This will cause the rabbit to stop eating and can be very bad.
If veggies are so good for rabbits, why do so many people that feed them raise concerns about diarrhea? That's because they aren't as good for the rabbit as most people think. Just because they are good for people and just because the rabbit likes them doesn't mean they are good for rabbits or that they should make up a staple in the rabbit's diet.