To me, that doesn't prove that he wasn't already converted.
You've never known an already converted person to weep bitterly over a sin they commited, or done so yourself?
I'm sure David wept bitterly over his sins.
I'm sure Abraham did too.
And others.
No one weeps bitterly over sin after conversion?
Peter sinned after this too. That's why Paul had to confront him. He was being a hypocrite, telling others to live in a way he wasn't. That wasn't being very humble.