With a medical diagnosis of autism, you should be able to have his physical therapist and/or his physician write a "justification" or a "prescription" for a larger stroller. As a special education teacher, I've helped with documenting that a child is unsafe (does not respond to "Stop" or "no," won't hold hands, runs, etc.) and as a result is prohibited from (or limited in) participating in the community. The form then is submitted to your insurance/Medicaid so they will help pay for this as durable medical equipment. You will probably have to argue your point but most PT's have experience with this.
MaClaren makes a LARGE (130 lbs.) umbrella type stroller for kids with special needs called "Major Buggy Stroller," but they don't come cheap ($400 and up). There are several other mfg. - trying searching "special needs strollers."
If you have not explored SSI/Medicaid options, I would also encourage this. In Nebraska and Mass., these programs help pay for daycare and "respite," have a data base of trained providers, and provide/pay for other services/items (diapers after age 3, Pediasure, etc.). Once they got passed the idea of "I'm applying for welfare," the families I work with are grateful for the services/opportunities provided by or that they learned about as a result of applying and being accepted.
Good luck!