Cognitive load is a major factor affecting user performance. Hence, a better understanding of cognitive load can help design better information systems. To achieve this goal, in this study we looked at the relationship between cognitive load and pupillary responses for a task that required people to either read a text passage from an actual website or read the simplified version of the same text passage. The simplified text passage was constructed in a way to assure reduced cognitive load, that is, to facilitate communication of textual information in a way that it can be read and understood easily and quickly. In our previous study, we showed that by applying a set of plain language standards (PLS) to online passages we can simplify the passages in a way that they induce less cognitive demand and hence can improve performance. In this study, we extended our research by investigating time series analysis of eye-movement (pupil dilation) as a proxy for measuring cognitive load during reading these passages. To this end, we conducted an exploratory analysis in order to understand how text simplification, which was used to reduce cognitive load during reading, affected pupil dilation over time. Our results show that text simplification had a significant impact on pupil dilation and that it affected pupil dilation differently at different reading intervals. Additionally, our results show that examining pupil dilation during fixations and saccades separately can provide new insights for understating cognitive load.