Nah, you don't sound greedy. It sounds like he's having troubles managing his resources.
When one has multiple relationships, one has to figure out how to manage all of the resources--emotion, time, attention, money. If you can't manage your resources well, then it's unlikely all of your relationships will last.
When I was involved with a gf, I spent less on myself so I could spend some on her and her children. As my wife and I maintain separate finances--splitting the family bills and taking care of personal bills and fun stuff out of personal funds--my obligations at home were covered. I still occasionally picked up something for my wife, and I was also able to occasionally pick up something for my gf.