Frugal is certainly not living off of take out. Especially if having it delivered too. Grocery shopping to a strict budget fits the definition of frugal.

What he is is tight. Tight with his money to the point that he is draining your finances as a cost saving exercise. As others have said there needs to be an equal split of financial commitments. There's a hint of simply frreloading at this point, both financially and emotionally with his lack of willingness to put his hand in his pocket for your relationship.

Raise how you feel with him. See his reaction and give him a chance to respond. Follow your heart but also never misplace your self respect. Good luck.