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.

The SPA data should be also weighted using the weight variables included in SPA data files. There are facility weight, provider weight, and client weight, depending on your unit of analysis. For example, if you link DHS data to the regional level SPA indicator: proportion of health facilities that provide Cesarean delivery services, you would use the facility weight.

Hope this helps!

From your previous description, I understood that you want to examine how access/quality of healthcare is associated with infant mortality and you plan to link DHS and SPA data at the regional level, right? If this is the case, I see the following major steps of the analysis and the weight variable you would use in each step.

You first need to generate health service variables of interest at the regional level based on SPA datasets. For example, you want to look at the availability of C-section services in the region, you may generate this indicator: proportion of health facilities in the region that offer C-section. When generating this indicator, you will use SPA facility weight. Sometimes you also want to use provider data, for example, % of facilities with at least half of the providers who provide delivery services trained in C-section. You will need to use both provider weight and facility weight to create this indicator.

After you prepared these SPA indicators, you then merge them into the DHS dataset, for example, BR file using the region variable. You do need to make sure the region categorization is the same between DHS and SPA for the same country. They are not always the same.

After merging, let's say you use survival analysis to test the association between healthcare access variables and risk of death before one. You will apply the DHS weight.

Hope this helps!