Wow... I hear so many stories of property managers and landlords doing things that I've never had an issue with. I moved Gunther into our apartment without a pet deposit or limits on weight because we were moving and the property manager had no issues or arguments with that. I don't see why your pup can't stay with you until either 1. you move or 2. he reaches the max weight allowed. Right now he's not at that weight so I don't think they can force you to get rid of him, especially once you've given 30 day notice that you're moving out before the dog reaches that weight. Eh, regardless, happy to hear you're reuniting with your puppy. I would be worried about the outdoor thing too... I refused to let Gunther go out at all before he had his vaccines. But parvo is high in my area.
Hail Gunther 7-2-2013
If at first you don't succeed, destroy all evidence that you ever tried.