Small merchants negotiate with Stripe for a flat fee to accept all cards. Big merchants negotiate with the networks and pay varying prices for varying rewards amounts (or however they get the deal structured).
also milage reward points can hit as high as 2.3 cents per dollar so assuming i want to fly to japan with ANA i could in theory get 8.6c in value of MR points per 2.6c i charge myself. However i would not expect to get away with this and i'm sure square would figure this out.