For any points weld operation to work, the meshes with the verts to be welded must be part of the same object. To do that, select both and weld them - not points weld!
Mass welding jagged edges using average weld is pretty tricky because, as you increase the influence distance, you could end up having two verts on the same mesh which are closer than the two points on the separate meshes you intend to weld. It is really intended for a fast operation where the edges to be welded are on the same plane and pretty close together.
One thing you could try if this won’t mess up the shape of the polys you want is to loop-select one of the edges to be welded and make the distance on the plane of interest - must be in “world” mode - 0. Do the same to the other then loop-select both and move them close together. With the edge-loops still selected, change the selection to points and do the average weld. This will only affect the selected points.
Hope I’ve managed to explain this OK