His arm is basically in unused factory condition but will need to be brought up to strength through a throwing regimen.
His weight leads me to believe he’s significantly overweight since most 12-13 year olds I have worked with are in the 100-140 pound range of various heights. His height is above average for his age and he should still have some growing to do. Adding muscle will help him burn away the “flab” that much quicker. Controlling his diet and only slightly increasing his exercise will get 10-15 pounds off him by Spring. He needs to get that discipline from his parents to start with. Once he sees the results, he will buy in to the plan. His confidence and self-image will improve and those are both big take aways that he’ll need to possess by spring time.
As for having his imbalances assessed. That certainly can’t hurt, and if he is serious about maximizing his baseball potential, it’s something to strongly consider.
As for the arm, you have plenty of time. I’d try to gradually build him up to 80-85 pitches over a 7-8 week time span and then sustain him at that level throwing every 5th day at that upper number until you shut him down in October. At the beginning, he may get warm, get his arm up to game speed then throw two sets of 10-15 pitches. Then every 3 days add 5 pitches to the total provided he can easily accomplish the increased workload to a max of 45 pitches. If he can’t reach a goal, then hold at whatever level he’s on for one or two sessions (remember, you are in no hurry) then try again to add to the workload. Once you get over 45 pitches now you are resting 3 days and throwing on the 4th. Once you get up >60 you are resting 4 days and throwing on the 5th from then on. Halfway through each rest period, be sure to play catch and get the arm warm to keep it loose and help it heal properly between bullpens.
Keep the bullpens as game-like as possible. Keep the pace between pitches to a game pace. Many people rush through their bullpens and are done in 5-10 mins. There should be no less than 10 seconds between pitches and no less than 5 minutes between sets. In a game it will be probably closer to 10 minutes between coming off the mound and going back out. A pace of 3-4 innings per hour is average, so there is no need or benefit of rushing through your pen. Each set should have a focus. That is the only significant way that the pen should differ from the game. In a pen, you may throw 10-15 consecutive down and away fastballs. Then you might come back with 10-15 down and in fastballs. Bullpens allow you the opportunity to refine your pitches so that you may call upon them when you need them in game situations. The worst type of bullpen is throwing random pitches to random locations. To me, you may as well not throw that bullpen, if you are going to flush it down the toilet.