Why does paddle blade size matter?

I have a very basic understanding of physics, and I know next-to-nothing about foils and wings. So I was hoping someone could explain to me why paddle blade size matters.

From what little I understand of a wing paddle, if used with proper technique,  and when a good catch is achieved, the blade is somewhat "locked" or "fixed" in the water and the paddler is pulling/leveraging themselves and the boat past the fixed blade. If this is the case, wouldn't any size of blade that can be "fixed" provide the same platform from which to pull/leverage yourself past the blade?

I assume that there is a bunch of factors I don't understand, such as "slip", and the sideways motion of the wing blade as it moves away from the boat. So I'm hoping that someone can explain the difference in all the various factors at play between a small and large sized blade. Ultimately, does a large blade require more energy from the paddler and potentially result in faster speeds? If so, why?

From basic physics I can only think of "for each action there is an equal and opposite reaction". So basically,  as the paddler applies force to the blade to go forwards, there must be some force going backwards-- i.e. the blade is not really "fixed" and  the paddler is moving water backwards. If that is the case, a larger blade could move more water backwards???

I found this, which was super helpful:

PaddlingScience | Wings, Bernoulli and Blade Locking

And this:

PaddlingScience | The Effects of Blade Size on Performance

The author concludes that water is indeed being sent backwards, as per Newton. A bigger blade would push more water backwards. He has a nice analogy:

"Any canoeist who has ‘wash hung’ behind a motor boat will be aware the propeller is blasting a lot of water backwards, and not simply ‘screwing’ itself forward through stationary water."

Thanks Mike Phillip, who authored the above pages. Not sure if it is correct, but seems like a useful and thoughtful explanation!

I have read those mike phillps articles before and really liked them. I think they clarify a lot about how thing wing works. 

If we had perfect, indestructible bodies, I think the best paddle would be the one with the biggest blade. 
The blade enters the water - there is no 'lock' on the water until it starts to move - and for a wing blade, move so that there is flow over the back of the blade. 

It is instructive using a blade that is very big. It is very hard to accelerate, much more difficult than with a small blade. For many of us, we get better initial (first 5 strokes say) acceleration with only partly burying the blade and making very very short strokes. Not efficient, but better for acceleration. 

As the boat gets up to speed, we can transition to catch, lock, push boat past blade, recovery. 
Try this with a very large blade. It feels efficient, but the strain on joints can be felt. Drop to a smaller blade; there is a drop in efficiency, the stroke feels a bit 'spongy'; but the strain drops as well. We can sustain effort for longer.