The bizarre part is that he calls on the button with 10,3. Your play is fine i think. Most of the time against weak opposition an overbet means a drawing hand that they are overplaying (flush draws regularly) or a TP/ shit kicker scenario. Also overbets preflop tend to be hands that are v.tricky postflop, so JJ with good opponents and small pp's with weak opponents.
Sometimes good players overbet the pot to ensure draws arent getting the correct odds even if the pot gets multiway. Threatening someone's tournament life gets rid of them quicker. Hard to explain but ill give it a stab. You have AcKd UTG +1. Stacks are 2000pts deep. You raise preflop to 200 with blinds at 25/50. You get 2 calls from loose players who you kow like to chase draws when getting close to the correct odds.
Flop comes As

. Sometimes if the pot is already large enough to warrant taking down (ie here its 675), overbetting simply means that your chances to win have gone up enormously.
Contrast this with a pot sized bet. Say caller 1 had

. If he calls thats fine. But now caller 2 with Js7s thinks he's getting a good price and calls too.
Pokerstove analysis means that in this case ur a 62% favourite against the 2 hands.
Against the 1 hand (AJ) that would probably call an all-in bet, ur a whopping 98% favourite.
Overbetting simply means that drawing hands are getting nowhere near the correct price. This means that you are letting them make and awful mistake if they weant to play on.
By making a pot-sized bet you are allowing the second a caller a 3-1 shot with a flush draw that he SHOULD take.