Every context-free language has either polynomial growth or polynomial growth:
In the notation of the question poser:

* Either there is a polynomial $p$ so that $w_n\le p(n)$ for all $n$
* Or there exists a $c>1$, so that $w_n\ge c^n$ for infinitely many $n$.

This has been shown for instance in:
> Martin R. Bridson, Robert H. Gilman:  
> "Context-Free Languages of Sub-exponential Growth"  
> Journal of Computer and System Sciences 64, (2002), Pages 308-310