He is average height and average weight

He is average height and average weight
 

I know that to say to be average height is Ok, but never heard average weight is that OK too?

Yes. "He is average height and weight." is a perfectly normal statement.

Should it be "He is of average height and weight"? Is the "of" necessary here?

You are of the right opinion. :thumbsup:

One doesn't say 'he is height and weight', and adding an adjective doesn't change matters.

Haha. Yeah. What they said!