I passed thru Sweetwater a year and a half ago on a road trip to Fort Collins. Fortunately or not, It was not meal time either time I sped by so I didn't stop, but I had made note of a couple of places that were of interest to me if I was hungry. You may have already found these:
Allen's Family Style Meals - judging from the pictures, this is the dictionary definition of 'humble eatery.'
There does appear to be a pretty full array of known, national fast food chains in Sweetwater.
Daniel Vaughn of the Texas Monthly BBQ Blog has posted 3 brief articles about Big Boy's Bar-B-Que - this is the main one; the other ones have pictures of the food if you want to look them up.
If you have time to get away, Abilene is just forty miles east on the Interstate. Abi Haus was one of the most interesting finds I came across in my research for the whole trip but both times I passed thru I missed their limited serving hours. And it closed earlier this year but has recently reopened with some changes to the menu? The website is inactive but you can find a little online on Yelp.
Lytle Land and Cattle Company in Abilene was recommended by two people; the grilled quail got high marks.
Perini Ranch steakhouse in Buffalo Gap would also be worth a drive, apparently. It's off the Interstate but Texas has good secondary roads. That would be about a 45 minute drive.