1.
If you check up on something, you find out information about it.
It is certainly worth checking up on your benefit entitlements...
The Government employs tax inspectors to check up and make sure people pay all their tax.
PHRASAL VERB : V P on n , V P
see also check-up
2.
If you check up on someone, you obtain information about them, usually secretly.
I’m sure he knew I was checking up on him.
PHRASAL VERB : V P on n