Side reins aren't very effective at building a topline, they just set the head. First a horse must be generally well muscled, then you can begin to build the topline.
So first get him into condition, if he isn't already. I start off with a routine of 3min walk on each hand, 3min trot on each hand, 2min canter on each hand (with a break between minutes) and then 5min walk on each hand again. What you want to work towards is 5min walk on each hand, 5min trot on each hand, 5min canter on each hand, 5min trot on each hand, back down to 5min walk on each hand. Once your horse can do this without dripping in sweat after your lesson you'll be ready to work on individual muscle groups, like the topline.
Again, you'll first want to build the topline from the ground, that way your horse will be able to continue strengthening it under saddle. I like using a chambon, although there are other training tools out there. At first let it be very loose, to give the horse time to realize it's move comfortable to wear if he stretches out, reaches under himself and lowers his head a bit, but it doesn't cause him severe discomfort until he realizes this. Once he's got the basic idea you can begin shortening it (very gradually!) so he'll work more. I generally replace the 5min canter of a routine without any tack with 5min of trotting with a chambon (trot is best since the head moves the least in this gait). But remember, tack items like this are just training tools, the horse should only wear them to help him build up muscle and improve his form, it's not a permanent solution to have him move in a certain way.
Good luck!