Lifting light weights has the potential to increase muscle size, even if the weights are pretty light.
However, the key is that when lifting light weight you might have to go closer to failure than you would have to when lifting heavy weights.
This is an important concept, because just lifting light weights with submaximal loads might not be triggering a large enough response to create adaptation.
Instead, think about a muscle growing trigger in terms of how close to failure the movements are and how heavy the movements are.
If you aren’t seeing the progress you like, it might be because you aren’t going heavy enough or you aren’t doing enough reps.