Welcome aboard, Joanna! Congratulations on your first cruise with Disney Cruise Line!
Castaway Cay is one of my favorite places in the whole world. Disney's private island is a real paradise with so much included that you can spend the whole day there busy and still not experience it all. Plus, there's a lot of relaxing to be done on Family Beach and Serenity Bay, so you can spend the day however suits you best. We do love renting bikes to explore the island. There is a great bike path that heads out the old air strip and into a bike loop in the center of the island, and another bike path at Serenity Bay at the end of the air strip that heads down a shady path along the far side of the island with beautiful ocean views at the end! My kids always make sure we stop half way through to climb to the top of the observation tower where we can see all of Castaway Cay and snap photos! Don't miss that hidden spot!
I checked with the agents at Disney Cruise Line about weight limits for the bikes, and they don't have any listed in particular. What I would suggest is not to pre-reserve the
bike rentals online before you go. For any other Port Adventure (except snorkeling which can easily be booked on the island too), I always suggest pre-booking as they do fill up quickly. But, there are plenty of bikes on the island so you can easily walk up that day and rent then. If your husband is comfortable riding a bike at home, it would be the same there. He may want to head to the rental spot and check out a few of the bikes to make sure before renting. If you decide to skip the bike rentals, you can always walk the bike loop. There is a tram that takes guests out to Serenity Bay, so you won't miss experiencing the Adult Exclusive beach either.
Have fun planning your cruise, Joanna!
Marcy