I haven't tried it. At just under 10 oz it isn't an especially heavy (or light) solution, but seems about average or slightly lighter than average.

The video says the main purpose is only to filter out the taste of chlorine bleach (Clorox), after using it to kill any nasties in the water, so you'd also need to factor in the weight of the Clorox and container you kept it in to arrive at the total weight.

It also seems to rely on a wide-mouth bottle, for which you'd have to experiment to see which bottles would work best. The hard plastic bottle in the video would almost certainly contain BPA, if that is a concern to you, and is not the lightest solution to water storage.

Using bleach to purify water can also create some undesirable chemical byproducts as the chlorine reacts with organic compounds in the water. I don't know if the Brita filter would remove these. The byproducts are carcinogenic.

On the whole, the system demonstrated in the video should work to eliminate any bacterial contamination, and provide you with OK tasting water. Not sure I'd recommend it wholeheartedly.