The only 1 know of off the top of my head is the Anaheim Plaza, walking distance to the parks, the rooms have small fenced areas if you are on the lower floor, they are large and the rates are reasonable. I've never taken my dog tho.
The Anaheim Sheraton (the one that looks like a castle) also takes pets...and I'm thinking no weight limit since a bunch of my Dog Show friends stayed there on my last visit & we went to the Dog Show my last weekend...and one of my friends shows Bloodhounds (80-ish lb. dogs)
We just came back from a trip last week and stayed at the Anahiem Plaza. There were several people with dogs there. If I was going to take a dog I think I would try to stay there, as they have the nice patio areas on the ground floors, as well as a lot of nice grassy areas throughout the property that would be nice for someone wiht a dog.