Fine-tuning is the prevalent paradigm to adapt pre-trained language models to downstream tasks. Lightweight fine-tuning methods, such as prefix-tuning, only tune a small set of parameters which alleviates cost. Such methods were shown to achieve results similar to fine-tuning; however, performance can decrease when the inputs get farther from the training domain. Moreover, latest works questioned the efficiency of recent lightweight fine-tuning techniques depending on the task and the size of the model. In this paper, we propose to evaluate the generalization property of prefix-based methods depending on the size of the pre-trained language model in the multi-domain setting on data-to-text generation. We found that their performance depends heavily on the size of the model.