Need advice on a man child.

My boyfriend plays his video games until 4 in the morning leaving me taking care of the baby all night. I wake up at least 3 times to either change his diaper or get him some water (he’s 16 months). Sometimes he’ll wake up for hours in the middle of the night and that’s legit the only time I get any help. I work 4 days a week 3pm-10pm and one day a week from 9am-7pm. He currently does not work due to hurting his wrist.. been out for about 2 months now.

My son wakes up anywhere from 8-9 in the morning so the days I’m off or the days I don’t go into work until 3, I’m stuck doing EVERYTHING until the boyfriend decides to wake up which is usually not until noon. It’s really pissing me off because the only reason he sleeps in so much is from video games. I’m sick and tired of it. I tell him he needs to get off at a decent time so he can help me with OUR son. He doesn’t clean, when he does its half ass. He doesn’t cook.. his idea of cooking is hotdogs. So I get worried about him not feeding our son properly while I’m at work. Overall I’m just over it. He’s not doing what he needs to do as a dad. I feel likes it’s the bare minimum with him.

Edit to add: the reason he’s not back to work is because he has to wait for his dr to clear him. Or else I’d be pushing his ass out the door for not getting a job!!