I usually play as a low fitness character and i was curious how body weight and fitness skill affects time you can jog. I did some tests in debug mode and is seems that overweight makes you loose endurance 2x faster (not exactly), while obese only affects your fitness skill (as you can see in description and even on old wiki page), so character with out of shape + overweight (3 fitness + 90kg) looses endurance faster than obese (3 fitness + 105kg), in fact obese doesn't change anything other than starting fitness. Character with normal weight and fitness lvl 0,5,10 will do the same as obese character with corresponding fitness lvl. For the bonus underweight and very underweight doesn't affect your fitness either besides starting fitness skill. All tests based on jogging only.