Maybe I'm quoting the wrong part of the video but he suggests you need to use the re-usable heavy bag six times not hundreds of times to equalise the environmental impact?

This looks about right to me - he's comparing with the very heaviest re-usable plastic bags which I could imagine have at least 6 times the mass of the single use bags.

I typically use the lighter re-usables plastic bags - unless I need to carry a lot of heavy stuff - which are maybe half the weight/thickness of the ones he uses for the comparison.