Hi Andee. I posted a response to your other forum post with the same question. I have copied and pasted my response below. Here is a link to the other post.
This help page from UCLA is a good introduction to different types of weights in Stata. Typing “help weight” in the Stata command will also lead you to a help window on how to apply different weights. IPUMS provides some sample code for using weights. This page from the IPUMS NHIS user guide includes some sample code for using weights, subsetting your analysis (such as by age), and accounting for sample design when using weights. Also, this page from The DHS Program is a good resource that walks you through how to use weights in multiple steps.
Even when using weights correctly, you may see large intertemporal changes in individual countries when calculating certain statistics. This can be due to a variable having a high level of measurement error, a sample size in a particular country being small, or the universe of a variable changing over time. Literacy rates may also change substantially over time, especially if the DHS surveys are several years apart. I would also double check your code to ensure you have recoded the literacy variable correctly. You can check to see that it is recoded correctly by tabulating the variable, looking for whether the possible values of the variable are what you expect and intend (0 and 1).