Need buffered point to extract raster pixel value when overlapping >1 pixel

Hello,

I have a raster of 25km2 and point features with lat/lon. I have successfully extracted all raster values with the points in the lat/lon data set from the raster, but then wanted the points to be buffered by 1nmi, I can't seem to find a way to have the buffered area extract the raster values. What I want is to be able to so is get the average (weighted?) for the raster value when a buffered point overlaps one or more raster pixels.

Is this possible?

Thank you for any clues or direction!

And Happy Thanksgiving to ALL~

~Alice