Only Use Suggested Photo Sizes
According to guidelines from Facebook itself, there are several "supported" photo sizes: 720px, 960px, 2048px (all listed by width). If you can get your .jpgs to one of those sizes, you'll be good to go with minimal compression issues. For profile pictures, you'll probably want to go with the highest size, 2048px (just note that Facebook also advises to only upload with the "High Quality" setting selected with this size).
For cover photos, Facebook advises that photo files should be less than 100KB, with an optimal size of 851px by 315px.
With these tricks in your arsenal, your likes are guaranteed to increase tenfold. Well, that might not be true... but your pictures will at least look way better.