The force that M places on wheel 2 is due to gravity. Now the wheel will push up on the force with the same magnitude, if there is no string.

Now the string has tension and the components of that force will point up and to the left. Friction cancels out the component pointing to the left. As for the vertical component, we know the block M isn’t accelerating so the sum of all forces have to be zero. Therefore,

Tension+F2-Mg=0

So, Mg=Tension+F2.

Notice that Mg doesn’t change with or without the string, but in the case of no string we have,

Mg=F2.

So you can conclude that F2 decreases when you have tension in the string pulling up on the block.