I sing to my dogs...they love it also! My boyfriend and I make up little songs about them and it's just so much fun.
Last summer, Rosco, my fox terrier mix, jumped the fence to chase a squirrel. I live near a mall and a cemetary and we searched and searched and searched, and couldn't find him. Called every vet, animal control, animal shelter, city police, county police, state police, humane society, and finally got a call the next day that someone had picked him up at the mall and had him at their house. Anyhow, back on topic, all I could think about when he was gone was that I would never be able to make up little songs about him and sing them to him, and that broke my heart.
So, I don't think it's weird at all to sing to your dogs!