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You can place a field on the Size shelf, but that effects the size of the line at the point. So if one point is "small" and the next point is "big", you'll see the line grow from small weight to heavy weight as it connects the points.
You could get the whole line to be consistent if you added additional rows to the source data:
so, instead of
Point Size A 1 B 2 C 3 D 2 E 1
, which gives you a line from A to B with Size 1 growing to 2,
you would use:
Point Size A 1 B 1 B 2 C 2 C 3 D 3 D 2 E 2 E 1
which would give you a line from A to B with Size 1, B to B (hidden) with size 1 to 2, B to C with size 2, etc...
Hope that helps!
Sure -- increase the Size shelf setting in order to increase the weight of the lines by a consistent amount (assuming nothing is placed on the Size shelf currently). If you're wanting to increase the Size of the line based on a specific measure value, you can place a measure on the Size shelf and use that to dictate the size of the line at various points.
If this doesn't help, please mockup a sample TWBX and attach it here -- you can use the Superstore Sales dataset or a sample dataset of your own to drive the sample TWBX. Cheers!