If you mean exercising with external weights like dumbbells or machines, use: Strength training Weightlifting Resistance training For Health Goals
If you are referring to fitness in relation to your size or body composition, use: Healthy weight Body composition Writing Weightlifting Notation weight fitness
Depending on how you want to use the phrase, here are a few ways to write "weight fitness" more naturally: For Bodyweight Training If you mean exercising with external weights like