Hi Julie,
Although I've never seen an actual weight limited listed on the Disney website or stroller rental locations, I called Guest Services to see if they had one listed.
The recommended weight for single strollers is 50 lbs or less and for double strollers, its 100 lbs or less. I will say that I've seen kids in all sizes in those strollers and if your kids are comfortable go for it. The parks at Disney are really big and I'm all for anything that helps my family navigate the parks more comfortably. Happy kids = happy mama.
Stroller Rentals are on a first come first serve basis and quantities are limited. Advanced reservations are not accepted. Rental fees are $15.00 per day to rent a single stroller and $31.00 per day for a double stroller.
A Length of Stay Rental Ticket will save you a little money ($13.00 per day for single and $27.00 per day for a double). With this option, you make a one-time payment transaction for as many days of rental as you will need. Upon visiting a Disney Theme Park, show your receipt at the stroller rental location and you will be expedited through the queue with a reduced wait time. Please keep in mind that these fees are always subject to change without notice.
Strollers must remain in the park from which they were rented but you are only required to pay one rental fee per day or use your Length of Stay Rental Ticket. If you plan to visit more than one park in a day, save your receipt and present it at the stroller rental location at the next park. Keep in mind that being able to get a stroller in the next park is not guaranteed because quantities are limited. The link above also lists stroller rental locations in each of the parks.
Wishing you many magical memories :-) Allison