Answer:
The tension will double and the acceleration will remain the same.
Explanation:
In order to solve this problem we must start by doing a drawing of the situation and by drawing free bodies diagrams for both elements. (See attached picture)
So let's analyze the first free body diagram. We can suppose the friction between the cart and the horizontal surface is zero and since we only care about the horizontal movement, we only take the horizontal forces into account. So we do a sum of forces:

since the only horizontal force for the first mass is the tension, we can say that:

Now we can analyze the second mass. We will suppose the positive direction of the movement will be in the downwards direction, so we do a sum of forces:

The second mass will be affected by two forces, which are the force of gravity and the tension, so the sum of forces will be:

Now we can combine both equations, so we get:

and now we can solve for the acceleration:



This ratio will represent the acceleration with the original masses. But, what happens if the masses double? Let's find out:

we can factor a 2 from the denominator of the fraction so we get:

we can simplify it so we get:

as you may see this is the same as the original acceleration we had found, so the acceleration remains the same.
What about the tension? We take the equation from the first sum of forces and double the mass.

since the original tension was:

this means that when doubling the first masses, then the tension will also be doubled.