Some suppose that the tick to which the simile “full as a tick” alludes is the bed-tick, the old-fashioned flat, rectangular bag of cloth which was stuffed with feathers, straw, or the like to form a bed.
It had to be full, of course, or one might find one’s poor bones resting on the floor.
But the tick that is really meant is the disgusting, bloodsucking insect that attacks the skin of man or other animal, burying its head into the flesh and becoming fat and bloated.