(I apologize for the silly question ahead)
I’ve lost some weight recently, and I was able, for the first time today, to close my belt buckle using a notch higher than usual…
For the life of me I can’t figure out if I “went up a notch” or “down a notch”?
Is this phrase even applicable for an actual belt?
down a notch means down a level.
It is used in sentences like
Turn the volume down a notch.
or, figuratively, in sentences like
Anyone who names a board game after himself needs to be taken down a notch or two.
Soon he was taken down a notch.
The expression you are looking for is probably to notch (something) tighter.
She notched her belt tighter.