You mentioned that he grabs it and pulls “as if you’re playing.” Do you play tug-o-war with him? This could be confusing him. If it’s ok to play with some ropes, then why not his leash? My pit loves to try and grab the leash and play with it too. It can be rough because they do get pretty excited and don’t always understand that it’s your hand, not the leash. It doesn’t sound as if it’s an agression issue, just more of an obedience problem. When my dog does this, I give a firm, “NO!” then choke up on the leash, pressing his nose. This forces him to release the leash, I then grab the leash closer to his collar so there’s no room for him to get ahold of the leash. If he continues to grab for the leash I give a sharp tug and say “no” again. This usually helps him understand that the leash is not a toy and I am not playing. Whatever you do, DO NOT try to pull the leash away from him! He will view this as playing! Try to give him a “no” and a sharp tug on the leash BEFORE he gets a hold of it, to remind him of his manners. Like I said, if my pit does get ahold of the leash, I grab the leash right by his nose and press his nose. He lets go every time. You have to be consistant though. Don’t let him play tug-o-way one minute, then decide it’s a nuisance the next. Also, if you’re leaving the leash dangling loose it could be tempting him, try holding it with only a little slack in it so that it’s not smacking him as you run, then maybe he’ll be less tempted to play with it. It would be a little bit different if this was an agression issue, but since it’s just a really obnoxious and rambunctios play issue, it’s just about getting your dog to understand that playing with the leash is not acceptable. We also got a chain leash, rather than a nylon one, for an amount of time. This can discourage the tug-o-war with the leash pretty quickly. At any rate, your dog just needs to be taught that this manner of play is unacceptable. Be firm and in command, then continue your run. Continue with obedience training as your pit is still such a puppy at heart! Mine is about the same age and he still acts like a puppy more often than not!
