Umm... the cage... can never be to large.
Take her to the vet, and they will be the ones to be able to determine whether or not she is really over weight and make sure she is healthy (the vet can weigh her and judge that weight against her size - my Romeo is only 705 grams - the average Moluccan is 800, if you go off of standard then she is underweight but she is small so her weight is perfect for her size).
As far as the crop area, you don't really know what it looks like when its empty. Romeo is a shredder so I can always see her crop, when shes done eating it looks just like that. In the morning (she has a sleep cage that I don't put any food in) her crop is completely empty and none existent until she eats again.
As far as the biting, well you just got the bird. Let it settle before you start asking it to step up. Really read her body language, she will give you clues that she doesn't want to be picked up (like moving away slightly) if you ignore this and you continue to try to pick her up she will bite you. She has no other way to get her point across other than expressing it physically, birds more often than not will tell you what they want passively first and if you continue to ignore it then they will bite. You also just got the bird (who doesn't sound like it came from a loving stable environment. Unstable environment = unstable bird) it doesn't trust you yet. Since you haven't yet established trust, she is going to be more likely to skip passive signs and go straight to biting (shes protecting herself), she doesn't know you yet. Let her come to you on her own terms. Let her decide how far you are aloud to go with her and if she acts in any way like she is backing off then you should back off as well and give her - her space (or you will risk getting bit). Birds are highly intelligent and don't respond the way a dog would. They need to have a say in what is going on and being done to them. As far as the cage goes, treat it as her domain. That is her space. Think of it as a teenagers room, your not going to just walk in unwelcome and everything be fine. One thing that has help tremendously with Romeo is that there are certain spots where she goes when SHE wants us to pick her up. She is hardly ever in her cage, we leave the door open. She has learned that if she wants us to pick her up, that she needs to come down and sit on the cage door. That is the only time (unless I need to put her up for some reason) that I pick her up. If she is not on the cage door then I leave her alone (I still talk to her and am around her but I don't impose myself physically on her). This gives her the say in whether she feels like physical attention or not (after you develop a relationship chances are your bird will constantly be sitting on the door waiting for you). She has also learned that when she wants to go back to lift her foot in the direction she wants to go and we just put her back. By using these tactics Romeo hasn't tried to bite - not once. Giving them a say makes them feel secure in their environment. You want to establish a level of respect that is deemed on her terms. Your just going to need patience and time, eventually she will come around (don't try to push it or move too fast). Don't expect too much to early. Some birds take months before they are comfortable (Romeo didn't even touch a toy until I had her for about five weeks - now she destroys everything). Establish your routine and stay as consistent as you can, this way the bird knows what to expect.