How do experienced people think about empty side pots?

Recent example. $10 NL. A couple of limps, then a very muppety player with very small stack, like $1.50 left, goes all-in preflop from MP. I have AKs behind him and call. Another player calls and we're basically heads-up with a pot of about 5 bucks. My opponent was also fairly short-stacked and has $4 left. The flop comes KT3.

The problem is that the side pot is empty. I'm pretty sure I'm ahead here, but betting into an empty pot feels strange. Do I just treat it as if the hand had a $5 pot and go from there, or not?

I did decide to treat it as if it were a regular $5 pot on the flop. So I bet out the size of the pot, which put my opponent all-in, and he called with 33 for the flopped set to beat me. (MP all-in muppet had 87s.)

Is there any other way to play my AK once the K hits in this situation?

More generally, how should I be thinking about empty side pot situations?

Any and all thoughts welcome. Thanks.

K3nt, I wouldnt think of this as an empty pot, there is $5 that you want to win vs your muppet friend. By checking here you are allowing the other player to have a chance to catch and take your pot. I bet this pot every time, you are more likely to win the main pot vs one player than 2. It is very different if you miss, there is no reason here to bet an unimproved AK, since it is doubtfull that A high is the best of the 3 hands, but with TPTK you are more often than not holding the best hand.