Ginger, When you're pet travels with you in the cabin, it's not the weight that matters but whether he/she can fit in a carrier under the seat. Continental has always had a very clear policy on traveling with animals. You might want to check out the information on their
site here.
Dogs are definitely not allowed on the beach in Playa. I know people who take their dogs to Xpu-Ha beach on the weekends. You can definitely walk your dog around town though. Technically, dogs are not allowed in the outdoor seating areas of restaurants, but you do see it -- though less and less over the years.
I think it's sweet of you to consider bringing your pet. The traveling part might be a little uncomfortable for him for a little while, but then he gets to be with his family the whole month. Small price to pay.