I know that て can be used before いる, as well as when asking for ください, but I just realized I don't really know what it means. For instance, I just read an instance of て being used at the end of a sentence:"知り合いもいるからちょっと待ってて!" What exactly does the て form mean in this context? I know it's short for いて, but even so, I've never ended a sentence with a て form verb.
In general, a standalone TE-form of a verb can be a request. You can essentially think of it as 〜ください being assumed.
In this specific case, it is 待っている that is being conjugated into TE-form, with the い getting omitted since it is casual speech: