Even with a lightweight tarp the issue is that any tarp, and any cording crossing diagonally across the middle, will always always always sag at least a little in the middle. The ONLY way to prevent that is to have some kind of rigid support going across diagonally between at least 2 opposite poles or to have a center pole. NO way around that. It is just the nature of the thing. I have never seen any cord or tarp that has no sag, if only just a very little bit of sag. Even if there is only a foot between the poles there will be sag. Maybe not readily apparent but still enough to detect when compared with a true straight edge or line of sight. If water can collect in that very slight sag then it will collect and cause the sag to increase to collect more water.
The only other way to ensure no pooling of water in the middle is to not even try to have a center flat area to begin with. Instead slope both sides to allow run off or set it up as a lean-to with one edge high and the entire tarp angled back for run off. In all cases there WILL be some sag between all the poles so it's a matter of eliminating that bowl or at the very least angling the bowl to allow run off.
BTW- per the post above, you will notice in the photo I posted one of my shorter poles, the white one, is several inches shorter than the other short pole. I've tried many different configurations with 2 or 3 or 4 tall poles and settled on the one in my picture as being the best to avoid collecting any water. Sometimes I'll leave that shortest pole out and just run the cord out to a peg. All cords are tied off using the truckers hitch and sometimes get adjusted to tighten them after a few days.
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