According to this Research Highlight at Nature.com, it seems that our favorite big yellow bird is more likely to be a lady-bird.
J. Zool. doi:10.1111/j.1469-7998.2009.00596.x (2009)
It seems that the constraints of egg shell strength conspire to limit how large a bird can be without crushing it's own eggs. Males of larger species tend to be smaller, and this may allow them to incubate their eggs more safely.
Fun Facts About Big Bird
Description : 8-foot-2-inch yellow bird
Birthday : March 20
Likes : Singing, finding solutions to problems, roller skating, making people feel better
Dislikes : Making mistakes
Favorite Food : Birdseed milkshakes
Favorite Thing : His friends
Favorite Toy : Radar, his teddy bear
More bird stuff from Nature here.
[Images Muppet Wiki]