There is no term "weighted sampling" in survey statistics world. Not at least that I know of. It is like "use Excel to prepare a JASA paper". I guess people meant "unequal probability sampling" when they tag their questions with this dubious phrase, and then it just propagates like "Free Wi-Fi" network in the airports (if you don't know this urban legend: somebody just created an ad-hoc network called "Free Wi-Fi", a bunch of stupid computers connected to non-discriminantly, and so after a little while this network used to be found in every US airport for a few years, even though there was no Internet access or anything; sort of performance-degrading virus).
Anyway, I hate this tag, and would like to kill it. Any comments on this wild desire? My understanding is that I would have to retag all of these questions though. A more generic
sampling would be a better fit for most of them (and I believe I worked on that tag earlier).