Depends on how much you store in it. Don't go by "dry weight" - go by GVWR of the trailer. I suspect you will not be able to store as much in the PUP (popup) as in the HTT, so you will probably be pulling less weight. However, that lower trailer will have much less frontal area than the HTT, and will be much easier for your minivan to tow. Still no guarantee your minivan will handle it well (ours had trouble towing our (much smaller) popup up long steep grades, and we also had several major surgeries done on the transmission while we owned the minivan) but the popup - even this weight - will be a far better choice than the HTT for your minivan.
"Dry weight" doesn't include fluids in water tanks, waste tanks or even LP gas - any of those things will add weight, along with anything you store in the trailer. PUPs by their nature have less storage than any full-height trailer of any type, so you will probably store less in it, making the loaded weight less than that of the HTT.