Fitness is a skill that determines how much you can carry and your fatigue levels. The higher your fitness skill is, the more weight you can carry and the longer you can sprint before becoming fatigued.
Survivalist: Invisible Strain[]
Fitness influences your Stamina level. Stamina is used for running, fighting with melee weapons and fists, and breaking away from infected when they grab you. It also impacts how much you can carry.
Skill Leveling[]
There are a couple of ways of increasing the fitness skill. You can sprint for long periods of time or you can carry around Health and Fitness Guide that increases Fitness by 1 for each guide.
According to the developer, any action that causes fatigue increases the fitness skill, as does carrying a lot of weight while walking. Having characters haul items automatically will slowly increase their fitness.