... you may wish to invest in a stroller satchel. These have backpack straps that will allow you to carry the stroller on your back, hands-free. They run about $20 at BRUS; many other stores carry them as well. I find that mine is one of the best travel investments I've ever made. DS is now too heavy to use the seat onboard, so I use the satchel to safely check it.
(Heavy vinyl, and a good thing, too; the satchel got slashed by conveyor machinery at one airport, but the seat inside was fine. The airline replaced my satchel for me.)