Have to carry my big suitcase with me to the stadium to leave to the airport right after the game. Can I drop off a big suitcase at the Bag Check Facility as well?

Yes

They have bag check in at outside the stadium. Saw it yesterday at Broncos vs Jets football game.

Yes, you will have to check it outside the stadium

Theres a place out side the stadium at the Verizon entrance they will hold the for a fee.

No they do not allow any bags or suitcases at all. They do have a information number you can call but I do not have it at this time. I know you can look it up or go to MetLife Stadium web site.

I'm not sure a out a bag or coat check at the stadium. They probably have something. I would call ahead though to make sure you can leave a suitcase there during the game. I would be careful too about getting to the airport after the game. That place is a traffic nightmare and it typically takes significant time to get away from MetLife if you drive there. Research taking a train or express mass transit to the airport to save time. Good luck.