I think it is either: 1) a Happy Cooker; 2) a private labeled one Weber did for Sears or K-mart; or 3) a Weber but where the LID vent was changed out as there is a screw through the vent instead of a rivet. The LID vent has a large tab, but does not appear to have WEBER embossed on it, which is why I'm guessing it is something else, although I suppose it is possible that it is a Weber where someone either purchased a replacement vent through Sears or used one off of another grill. Either way, it should still be a good cooker & still has a lot of life left in it.
I think I remember hearing Weber also put out some kettles where you had to bolt on the vents yourself, but I'm guessing they still would have said Weber on the vent. I think one I have NIB might actually be one, but I've not really looked at it even though it is open.
Do you still have the old handles? Those might help tell the story.