Can't Edit Curves Of Particle System

Double-click the line to create additional keypoint. Then drag it to form the shape you need. Right-click menu allows to tune line behaviour near selected key.

Although being called particle system curves, it is in fact the curves of different properties of the particle system, e.g. Size over Lifetime curve, Size by Speed curve. So to see a real line(curve) in your Particle System Curves window, just clicking the Particle System GameObject in your Hierarchy view is not sufficient, you need to click one of those listed under Particle System Component in Inspector view.

The Editor tries to update the particle system as you attempt to move the node of the curve so if you don't have the latest computer there is a 20 second wait for the node to move a very small increment. It doesn't even move the curve to where you dropped it with the mouse. Crap Editor UI coding on Unity's part... The Unity engine and particles run fine on my PC in Editor and standalone build. It also seems like you can't change the curves via script although you can interface them. Wonderful, just wonderful.