It is probably weighing problem. But before you start tweaking, review your rigging. After all movements of body parts really follows the bone movements.
Here is my try. Lay the bone against real rabbit skeleton. Make sure all the hinge location is correct. In your case, it’s the pelvis bone that is giving you the problem; pelvis is large single bone and rabbit back flexing happen from lumbar. Not from middle of pelvis. The thighbone is located to the side of pelvis with ball joint. Thigh rotates from there.
Only other thing is the addition of breastbone. Since a rabbit backbone really follows closely by the back, automatic weighing simply don’t work too well. Chest and belly mesh gets weighed to arm and leg bones that are next to it. That is not what you want. Adding breastbone solves problem around the chest. Large pelvis bone will help for the belly.