Is there a limit to how large an airplane wing can be?
No, there is no theoretical limit to the size of a wing. You could make a wing big enough to lift the entire Earth (assuming, of course, you somehow had an atmosphere to fly it in).
There are, of course, many practical limitations to wing size. The lift a wing develops is proportional to the square of the scale of the wing, all else being equal. However, the weight of the wing (and the rest of the airplane it's attached to, for that matter) is proportional to the cube of the scale. So, if you double a plane's size, the lift developed by the wings goes up four times, but the weight goes up eight times. So, in that case, the wings would need to be even larger compared to the plane in order to lift the added weight. This is referred to as The Square-Cube Law (Wikipedia, Aerospace Research Central, TVTropes). You eventually reach a point where there are no materials strong enough to withstand the stresses imposed on such a massive wing.