Let’s say I have a spline with 3 points, S(tart), M(iddle) and E(end). I link a circle to the spline and put keyframes/waypoints at 0s, 1s and 2s: at 0s the circle is at S, at 1s the circle is at M and at 2s the circle is at E. With me so far? 
Now comes the tricky part. If I move M closer to E then at 1s the circle will be somewhere between S and M. However, at 1s I would like the circle to be at M (in M’s new position, closer to E), so that it would be going faster 0s-1s and slower 1s-2s. How can I do this?
Move circle to M in canvas at 1s? Or do you mean to have two waypoints, at 0 and 2s and have 1s automatically positioned between?
Set two waypoints and edit the first one. Play with Temporal Tension.
I’m making a long spline with lots of points.
Then I turn on anim mode.
Then at time t1 I add a keyframe and move the circle to the 1st spline point, then at t2 I add a keyframe and move the circle to the 2nd spline point, then at t3 I add a keyframe and move the circle to the 3rd spline point, etc.
Then I turn off anim mode.
Then I move those spline points around.
I want the circle to be at the new position of the 1st spline point at t1, at the new position of the 2nd spline point at t2, at the new position of the 3rd spline point at t3 etc.
Ah, I think I found it! I was playing around with the spline’s homogenous value, which did something, but not what I wanted regardless of how I toggled it. However, then I found circle->Transformation->Offset->Homogenous, which, when toggled off, seems to do exactly what I want. Yay! 