Well, as a native Spanish speaker, I would say "It may be worse" as "Puede ser peor" which is different to "Es posiblemente peor".
"Es posiblemente peor" is more formal, the kind of sentence I would expect from a doctor.
I barely use it with friends
Aloof, I was in Chile this month and peor also means worse off when referring to someone who is poor(er). But it can't be he is possibly poor because he = Él and poor = pobre. You must have been thinking Él es posiblemente peor :)