[A0566]

Well, I'm no headsup specialist but I guess I'll add my useless thoughts.

Some advantages to larger bets that pop up to mind for me:
1) Making their draws and calls unprofitable
2) Making more money off of value hands

So then for one I'd try to significantly pump up the pots pre-flop with value hands and optimize from there. (I don't know what the optimal strategy would of course be given as how I don't know the specific idiosyncracies of tihs player. The only thing that comes to mind is the generalization of "bet larger amounds but less frequently [so value betting] if he calls to much and bet less but more frequently if he folds too much.")

In other words, I'd try make calling much more profitable by getting much more money in pre-flop and outplaying them post-flop or stealing more pots pre-flop. [This is assuming that the player just stands still and lets you choose when the pot gets big and doesn't play back at you.]

It seems like with a loose-min-raise/bet player the optimal strategy would definitely not be a matter of trapping but utilizing a strategy that makes money over a series of hands with a smaller edge and smaller pots. Haha, basically the worst type of game against a rake that stays consistent with all pots.

You also said that he folds when you make big bets but only calls when he has it. I would then experiment to find what level of big bet makes him uncomfortable and try to exploit that somehow (By either stealing more pots with a bet size that makes the opponent's fold unprofitable, or causing him to loosen up too much and make money off of my value hands. Once again basic strategy. Why am I even talking?)

Then again, all of this advice is suspect because I suspect that I am horrible player.