#1 This is a robotics forum. Not an engine forum. So you would likely find a better answer elsewhere.
#2 An idler pulley is generally spring loaded in engine applications. The size of the pulley doesn't matter, because the belt doesn't wrap around the idler, the idler just pushes on the belt between two pulleys to tension the belt.
Here is an arm with a tensioner pulley on it. The arm will generally have a torsion spring on the non-pulley end that holds the pulley against the belt.
A better question is: what tension do you need on your belt. You need to pick a tensioner that will provide enough force.
As I said - take this to a car or small engine forum and you'll have better luck.