Shift lever tight when cable clamped in derailleur, adjustments seem futile
It sounds like the cable is not routed correctly, putting force on the cable where it was not intended and thus adding more friction than normal.  This would explain why the cable moves freely when there is no tension on it, and why it gets harder when you shift to bigger cogs.
Run down the cable from the shifter to the derailleur to see if the routing is wrong along the frame (or inside the frame).  Then check in more detail the routing of the cable from the last outer towards the cable clamp on the derailleur.
I can imagine that the routing towards the cable clamp is the most likely problem, as it's often not obvious what the correct routing needs to be.  Download the manual of the rear derailleur and double check your installation.
-- Edit below
I can't be sure which model derailleur you have, but the relevant manual should show how to route it correctly.  As an example I have included an image from a Shimano derailleur dealer manual.  Purely as an illustration you might note that the routing is different depending on the model.