Countering a heads up SB limper

I played my home game this weekend and we had a new guy playing. My home games are soft but this guy was definitely better than the average and plays postflop very well, and showed what seemed appropriate pre-flop aggression too.

However, when we got to heads-up, I noticed a curious change in his behaviour , whereby he limped the SB a great deal of the time. After analysing the hands post-game it seems he limps a very wide range (60% of hands) , with 20% raise/shove and 20% fold.

However, it's not like he's raising with his best 20% and limping the next 60% - some of his limps later were really good hands (AKo, K9s and 99), while he put down a fair few of his raises to re-raises indicating they were not necessarily his super premium range.

So i'm wondering how best to exploit this tendency, when a player limps a weaker range it's pretty easy to just bet, but this is a bit different.

This isn't going to help you, but he is playing a polarized range. He is balancing his premium hands with his junks hands to make it difficult to exploit. If you are not familiar with GTO, then that might direction to look in. I am too much of a novice to help. Based on the language you were using, you probably already knew this, but thought I would mention it just in case.