Ratings are percentage of potential viewers. Think of it as how the pie is split up. The size of the market determines how big the pie is. The Cardinals are in the bottom third of market sizes. The bigger the piece of the bigger pie, the higher ad rates can be.
But, that likely determines how much profit or not Sinclair makes. Unless there is a sliding scale in the contract, the Cardinals may be getting a flat payment from Sinclair each year. (I do not know this to be fact. It is just an educated guess.)
To the main point, I doubt the Cardinals are making considerably more from their TV deal than their competition. If that is true, it is may not be a huge variable in how much they can pay players. It feels more like a constant, which probably can be counted upon to help fund some base level of expense, including player salary perhaps. But even that changes when 162 games are not played. A lot of variables are in play.