For starters, I think the 4-jaw is more than enough chuck for that lathe. As mentioned, 4-jaws tend to be lighter because they've simply got less parts. I wouldn't hesitate to use that chuck at all. I haven't weighed them, but I know the 8" 3J on my 16" victor weighs more than the 10" 4-jaw I have for it. I have a 10" 3J for it as well, and that's way heavier than the 10" 4J.
As far as the 3-jaw, you've got a couple of things going on. It's hard to tell exactly from the pictures, but looks a touch big for that machine. I'm probably a bit biased, but at one point I wound up with an extra 6" 3J adjustable structure chuck and got an adapter to use it on my 14" Logan. I though the machine ran a bit smoother, with the 6" 3J on it than the 8" 3-jaw, and 10" 4-jaw.
I will say, whoever fit the backing plate for the 3J didn't really do what I'd call a proper job. For starters, having the adapter plate be larger than the OD of chuck simply adds unnecessary weight....and it looks goofy to my eye. They also seem to have left the adapter at full thickness and there's a long way from the face of the plate to where the spindle nose sits. Reducing the thickness of the plate will reduce the amount the chuck sticks out from the spindle and will help prevent chatter. The farther the chuck sticks out, the more likely you are to get chatter when doing things like parting where the's a lot of pressure on the cutter. You could face off something like 1/4" to 1/2", still have enough meat for the bolt heads and plenty of clearance to the front of the spindle. Next up, they didn't turn a hub for the back of the chuck where it has the recessed section. Adding a hub will help keep the chuck centered and you won't get chips in there like you do now (picture of the back of the chuck shows where those chips wind up.
I would turn it down to the OD of the chuck, then face off the extra meat and add a hub for the chuck to fit over. That will get the chuck closer to the headstock, save weight and simply work better.