How much does force increase if mass is doubled

First of all, the question is worded somewhat ambiguously because mass does not necessarily imply that there is a force (i. e. an object could be stationary in a system with no gravity and not have a force, or something of the like). Moreover, simply because an object is twice the mass does not mean the force will change.

However, we know from Newton's second law that F = ma. Therefore, force will increase or decrease proportionally with mass. This means if an object maintains a contestant acceleration and its mass doubles, the force that it provides will also double.

F=ma

So if m=1 then F=1m

If the mass were to double (m=2) F=2m

So if you are to double the mass, you are essentially doubling the force