It is based on whoever you check in with. If it is CO metal from EWR-CVG then you check in with CO and pay the fees based on that. If it is DL metal from EWR-CVG then you check in with DL and pay the fees they charge.

As long as the bag is checked all the way through to your final destination you only pay the fee once. If you were spending the night at CVG and collected your bag there then you would pay the fee twice, though some have claimed that a forced overnight and first flight out would not require such. That would probably depend a bit on the carrier.

I'd bet that you are going to pay the big fee with DL based on what you've described.