Is there a limit to the size of the universe?
My response has to be "It depends on what you mean when you speak of a limit..."
Do you mean "right now" or "ever"?
If you mean at this moment, the answer is yes - the universe has a finite size.
If you mean "Is there a limit to how large the universe could become?" the answer I believe is no. The prevailing view of the universe is that it is "flat" meaning that there is just enough matter to allow it to continue to expand forever, and only stop expanding when it becomes infinitely large (hard to think about!).
It's rather like a spacecraft that was given exactly the right escape velocity as it left the Earth. It will travel outward, slowing down, but at a rate that will only allow it to stop at an infinite distance from the Earth.
That said, I am not aware of whether recent thoughts on dark energy have brought this view into question. This is another question you may want to investigate.