I see threads all the time with aerating, rolling and thatching as the key to good turf. I base what I do after what golf courses do as even poor golf courses do a pretty good job. In a nutshell, kill the weeds and use a high quality fertilizer that is appropriate for your soil needs. Addressing the above:
Aerating Although this is a good idea, the homeowner does not have the equipment to make this practical. The golf course I play at had a deep solid tine machine that puned at 6" hole. Worked great but the attachment was $30,000 and was on a $30,000 tractor. A little out of my price range.
In order for rolling to work the roller must be very heavy, i.e. a small self propelled ones used for asphalt would work if the soil was pretty soft, again not real practical.
Thatching is just dumb for most lawns unless the condition is very severe which it generally isn't. Thatching is an excellent way to get weed seeds down to the soil where they can germinate.
Course of action,
1. Delay mowing the 1st time until weeds are actively growing, weeds grow faster than grass. Spray a good herbicide appropriate for the target weeds you have and use pre emergent, (prodiamine) at the same time. Cost for the Pre M is $30/acre and you can then select a better fertilizer appropriate for the soil needs.
2. Do a soil test and use high end controlled release fertilizer. Since phosphorous hasn't been in blends for going on 15 years it is lacking. Tests indicated that is was needed so an 18-12-6 with 2% Avail was used. The point is to make healthy grass, not fast growing grass. Apply at max rate, which in this 4#/1,000 square feet or 172#s/acre.
3. 2nd fertilize app if needed prior to hot Summer temps. This year things have looked so good I only did the front part of the yard.
4. Since #3 was not done, will probably fertilizer come September. Probably use 21-0-21 that is 75% Rxn controlled release.
Pics taken 7/30/2019 after a couple weeks of heat in the 90's and high humidity. This is not irrigated.