Holding up his head?

My son is almost 3 months old (adjusted age). He's still not holding his head as steady as I feel like he should be. I'm doing tummy time as often as I can for as long as he will handle it. But he just doesn't want to participate. He will only keep it up if I put him on his elbows. He won't pull himself up, he just lets his arms go backwards and won't pull them back up. If he does he just sucks on his fist or lays there and cries til I flip him back over.

Any tips??