It seems that George Owens and Mr. Belvedere butt heads a lot, but has George ever stood-up for Mr. Belvedere?

Sure he has. He must have several times (I haven't watched the show in a while), but one time that comes to mind is

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when he faces deportation.

Another is when another family rivals for his services, and all the Owenses face off against the other family to keep him.

And there's more than just "standing up for him", too. Occasionally he'll be sensitive to him and show understanding and/or encouragement.