In photoshop, saving on "JPEG High" gives nearly identical results to VeryHigh and Max settings which result in 2x and 4x larger files.
The same 1500x1500 source file was saved at 1500x1500 to these different jpg compression settings:
Max, resulting in size of 1,900KB.jpg shown below
VeryHigh, resulting in size of 751KB.jpg shown below
High, resulting in size of 410KB.jpg shown below
Med, resulting in size of 198KB.jpg shown below
Low, resulting in size of 132KB.jpg shown below