Second survey after knowing how different strata respond? We did customer survey in last fall from which we know how different stratas answer to survey questions. We did notice that amongst many strata having younger people who move often the non-response rate was much higher than amongst more established of our customers.  
Original survey was based on simple random sampling without replacement amongst strate and sample sizes strata-wise were based on proportional allocation.  
Should we use this information next time when we do customer survey? Should we allocate more for those strata which have more non-response. We could perhaps use some re-weighting to correct marginal distributions afterwards.  
Could this be reasonable approach?  
We have not done customer surveys earlier ourselves and previous survey was financed together with our industry association and we got only summary statistics. And survey was done by outside consultant firm. So we do not have any technical reports what they had actually done in that survey.
 A: The problem induced by non-response is bias due to differences in responders and non-responders. Adding extra observations to strata with higher non-response will not reduce the bias, so that approach cannot be recommended. However, adding extra resources, such as more personalized follow-up, is a reasonable strategy. I would not apply the resources to everyone in the sample of the low-response strata, but to a sample of the  non-responders, no matter what strata they come from. This technique is known as two-phase, or "double", sampling.
The overall choice of a sampling scheme, including the effort devoted to each phase of a double-sampling plan is governed by an equation which relates desired precision to cost. See any good sampling text, e.g. Lohr, 2009.
There are also weighting solutions for non-response, for example response-cell weighting and inverse-probability-of response weighting (IPW).  I'm traveling, but I believe that you will find good examples in Groves et al. (2009) as well as in Lohr (2009). Also, google "inverse probability weighting response" or related phrases.
References, both highly recommended:
Groves, Robert M., Floyd J. Fowler, Mick P. Couper, James M. Lepkowski, Eleanor Singer, and Roger Tourangeau. 2009. Survey methodology. Hoboken, N.J.: Wiley.
Lohr, Sharon L. 2009. Sampling: Design and Analysis. Boston, MA: Cengage Brooks/Cole.
