What I do.
After 1 or 2 firsts cut of the year. Couple days after a rain so the ground isn't rock hard. I leave my plugs cause they get chopped up with cutting. I then use a 10/10/10 fertilizer 2x a year
As far as weeds go, I have a friend of a friend that comes over every spring & when it gets to around 80deg., sprays my lawn for weeds & crabgrass. Then during the year I spot spray with a 2gal. Hand held sprayer to keep after an occasional pesky weeds that pops up.
This works for me & my acre of grass. Not picture perfect as an advertisement ad in a magazine but........... I'm happy with the results
Nik
Also, I de-thatch my lawn before aerating, & again early fall.