It's very important that you use the weights. Otherwise the within-survey distributions will over-represent the strata that were over-sampled, etc. The only question is whether, in the pooled file, you want to re-scale the weights. The alternatives are re-scale them to add up to a fixed number in each survey or to add up to a number that is proportional to the estimated population sizes at the times of the surveys. Between the two, I personally prefer giving every survey the same total weight. In a sense, THIS is the option that corresponds to not using weights at that level (but using them within the surveys). If you do not adjust for the sample size, then you are allowing a completely arbitrary characteristic of the survey to influence the importance of that survey. If you make the total weight for a survey proportional to the population size, then large countries will completely swamp small countries. Within the series of surveys, in many countries, the recent surveys are much larger than the early surveys.

But for many purposes you can just use the weights that are in the data. The issue of how to adjust the total weight for each survey is really only relevant if you plan to produce pooled estimates, such as "the mean contraceptive prevalence rate (CPR) in Ghana from 1990 to 2010" or "the mean CPR in West Africa in 2000". I don't think those are meaningful parameters to try estimate, and I don't think DHS surveys cover enough years and countries. If you are interested in estimating changes and differences, which I think is more appropriate, then you can just leave the weights as they are.