poise over (someone or something)
To stand in a steady, anticipatory position over someone or something. I woke with a fright to see my son poised over me, waiting with tears in his eyes for me to wake up. The cat poised over the mouse whole, ready to pounce the moment the rodent emerged.
poise over someone or something
to hover or hang over someone or something. She spent the entire afternoon poised over her desk, pouting. The dog poised over the downed duck, waiting for the hunter.