I am glad you found clarification on how to apply weights using svyset. We will revisit the data training exercises to ensure that the weight suggestions there are correct and/or document why they differ from the svyset approach.
Logistic regression can be calculated in Stata using the “logistic” command followed by the dependent variable and then the independent variables. Here is some example syntax from the Stata manual on logistic:
logistic depvar indepvars
The “logit” command also works with similar syntax where y is the dependent variable and x1 and x2 are independent variables (from the Stata manual on logit):
logit y x1 x2
For more discussion about completing logistic regression in Stata, see this forum post.