I have the same problem with my son, who is asthmatic and needs a stroller for the heat. The rentals are not really good for "big" kids, as they have to fold themselves in half or sit with their legs straight out in front of them. I found a Maclaren Volo umbrella stroller at Buy Buy Baby for $59.00 that holds up to 60 lbs, folds easily, is lightweight and comfortable for "bigger kids". Good Luck!
Have Fun!