Yes merchants pay a fee to processors for credit card/debit card transactions. They receive the benefit of more sales as some customers don't carry cash and they would lose those sales to other merchants. Merchants have to include this cost in their cost of doing business just like including the power bill or the rent or their employee's pay when pricing their goods and services.
What really irks me as a cash payer is that merchants pay a higher fee when a customer uses a card that has a premium on it. (you know, skymiles or some other such reward) so if you aren't also using a reward card you are subsidizing someone else.