...this big OF a wave ...?

I am used to asking

How big was the wave?

and answering

The wave was this big.

My question is that, I think, in the US, it is pretty common (I have heard the usage often) to ask

How big OF a wave was it?

and to answer

It was this big OF a wave.

Listen to 2:12 in this clip http://www.bbc.co.uk/news/magazine-31093276

I don't understand why the 'of' is there (Question 1) and I wonder whether this word pattern can be traced back to the time of the Mayflower (question 2).

I have also noticed this construction, and only in the last few years. I think it may be a generalisation of the forms:
I felt like a bit of an idiot.
How much of an idiot am I?