What is the benefit for the miner, of increasing the dificulty in a pool? I am part of a pool that allows me to set my own difficulty.
Increasing your personal difficulty doesn't benefit you much, with the exception of lowered bandwidth. Going from Difficulty 1 to Difficulty 2 will cut your upstream usage in half. From 2 to 4 will cut it in half again, etc., etc. Downstream bandwidth has a minimum amount due to work notices from the pool, but depending on your rate of share submissions, higher difficulties can also reduce that bandwidth utilization significantly as well.
There's probably some *extremely* minor benefits of higher difficulty due to miner overhead, and some earlier ASICs/firmware versions had problems when mining at lower difficulties due to the rate of share submissions.