People with higher leg strength will have an advantage anyway. Also, having to go back and forth will advantage people with higher agility. Randomly generated stats means some games will have advantages over others.
The reason I suggested you not bother with taking the items back is that since you've placed a time limit that's just wasted time going back and forth, not to mention that, as cow noted, the weight limit adds to the strategy. By the way I would like to stress that this is just a suggestion, it's your challenge.