The DHS survey weights are useful and appropriate for aggregating up to population-level statistics within a country, but I would be cautious about trying to stack DHS datasets and then do anything that relies on population weights. Of course if you are simply running regressions and looking for observational correlations and relationships, then weighting is probably neither necessary nor desirable.
When using DHS data, it is recommended to apply weights and more importantly to use the complex samples command in order to account for the sampling technique used (non-random). In SPSS you do this by going to Analyze - Complex Samples, then choose whichever statistical test you wish to run (i.e., regression, crosstabs etc). Before running any complex sample command, ensure you create the weight then apply it to your data using the COMPUTE command in a new syntax page. There is a comprehensive youtube video that gives you step by step instructions. Just enter keywords "DHS, weights, complex samples" in the youtube search box. Good luck.