The problem with carrying a loaded 'doggy bag' is not one of weight but simply one of convenience, if that is the right expression!
These proposals are reasonable and welcome when applied to urban and suburban pavements, parks, sports pitches, children's play areas etc, all of which need to be kept clean, and which are usually provided with waste bins. But once you get away from the suburbs and into the country, they don't really make much sense. Those of us who walk our dogs out in the Peak District or just around the bridleways and byways of the Goyt Valley, sometimes going for miles and taking a couple of hours or more (during which you never pass a waste bin) are simply not going to walk that distance carrying a bag of dog poo. We have a supply of doggy bags in our pockets, and we use them when we can, but when away from roads and paved footpaths we will have to continue doing what we do now, which is either to ensure that our dogs are off the track when they do their business, or (if they go where they shouldn't) simply flick or kick it into the undergrowth or (on the towpath) into the canal.
That may or may not comply with the proposed new regulations, but it is the reality of country life, and until the British countryside is fully equipped with waste bins, complete with teams of countryside rangers to empty them evey week (don't hold your breath!) it will carry on that way.