No one stands there in front of you all in class, and announces that for an (a substantial) increase in weight you WILL need an (a substantial) increase in power.
... Because that is an incomplete thought/statement.
I will
not need an increase on power, if I will accept a decrease in performance.
I have flown many aircraft at weights greater that the certified gross weight, as much as 130%, without the benefit of more power. I just expected less performance, (and I limited G) in accordance with the overweight authority for the flight.
So, no, I will not stand in front of class and assert that more weight requires more power - it just requires a "trade back" of something.