This is probably a regional thing but in the Midwest, at least here in Minnesota if you ask the barkeep for a snit with your bloody mary you'll get a large shot glass/lowball of beer.
I asked for one at a bar in California and they had no idea what I was talking about.
A google search said another term was Snert which I had never heard of either.
Does anyone know where the term came from? Is it common in your neck of the woods?