And that's how villain wants you to feel. You're supposed to be annoyed by their min bets while it puts you to the test and get info of where they stand and where you stand in a cheap price.
if blinds are low and and lot of blinds where u got lot of room for post-flop play and for future hands, min-reraise them. it backfires their annoyance. when they make a min-bet, they're pretty much trying to see where they stand by having u reraise them big, call, or fold. when you min-reraise them, which is only 2 blinds, they don't know where you're at. reverse their annoyance back at them. believe it or not, some people fold to min-reraise because they have complete air and don't want to continue their hand any further while perceiving your min raise as a reraise for value to get paid.
Of course, if I have a read that they'll fold to my strong reraise or if i have a hand and they act differently, texture of the flop, player's tendencies, etc, plays will vary. if villain is a calling station while you have a hand, then reraise big and build a pot as much as possible every street. but generally, if they min raise and become annoying while not having enough information or being complete lost of what i should do, i just min reraise. by doing this, they're annoyed as well because they can't figure you out either but they're priced in as well. by doing this, you can also get enough information from your villain.
However, if you don't have lot of blinds or short-stacked where you don't have lot of room for post-flop and future hands, you should be shoving/folding anyways unless u got a hand to slowplay or good hand to build.