my AR-15 has a 1 in 9 twist with a 16.25 inch barrel. What would be the best bullet weight for this combination?

Best is a relative term. We need to know what your going to do with your AR.

I found with my carbine I use a lot of 55gr FMJ Hornady bullets and Varget for general blasting and Sierra 69gr Matchkings and RL15 for accuracy.

Any bullet over 69 grains probably won't stabilize, although you might try the Hornady 75gr BTHP match. Sometimes that bullet stabilizes in 1/9 barrels.

Thanks. I just put a 1.25-4 scope on it and was sighting it in with 55gr FMJ Lake City and wasn't getting very good groups. I plan on loading some 69gr match kings this weekend.

I plan on using it for plinking and some light varminting.

Free floated barrel or standard handguards?

The standard handguards are not free floated and they will cause groups to open up when the barrel gets hot.

I have a regular 4 rail handguard at this point

They love 60 grain hp and v-max. 75 hdy should work when loaded near max.