5CD - Standing pat

Last night I was at my usual €5 tourney and a guy started to play in a very unusual way...
He stood pat on the very first hand without a raise and checked after the draw. He had 88xxx.
From there on he stood pat 17 times during the first half hour, with hands ranging from 66xxx through 3344x. Sometimes he just checked, sometimes he raised, sometimes he won the pot without a call. He lost most of these hands but won a few big pots with KKxxx or AAxxx. I only called him twice, with 2-pair hands, and won both small pots.
Anyway, by the first break he had doubled his chips, meaning the rest of the table, including myself, did not find a way to take the best of his weird 'strategy'.
What do you all think should be the best approach against this odd behaviour?