Dimensions, which nearly everyone underestimates
File size scales with pixel count, and pixel count scales with the square of the dimensions. Halving the width and height leaves a quarter of the pixels, not half.
So a 4000-pixel photograph displayed in an 800-pixel column is carrying twenty-five times the data it can show. Compressing it to quality 60 might halve the file and make it look poor; resizing it to 1600 pixels cuts it by roughly 84% and looks perfect.
If your compressed file is still large, this is the first thing to check and usually the answer.