You introduced your BOYFRIEND after 8 weeks?
He's staying over at 3 months?
He's sulking? Unsupportive?
1: you have been ridiculously naïve. Reckless even.
2: he's not a good man, you didn't know this when you introduced him to your child, but now you're seeing it. You now stop this ridiculous situation. NOW.
I was going to say 'No more sleepovers for at least another 3-4 months.' but that only applies if that person IS actually worth it, I don't think your boyfriend is.
Tbh, you need to bin him. He's a turd that'll never polish into anything. If he stops talking, goes cold, he's trying to manipulate you.
He's like this now? It will only get worse .
The only chance you have of regaining power here is to make your son the priority, state clearly that you won't tolerate silent/cold treatment for any reason and perhaps he needs to go off and consider what he wants, because you and your son deserve someone that is understanding and supportive.
Why is this bloke on his own? What is his relationship like with his Ex?