Health misinformation is a problem on social media, and more understanding is needed about how users cognitively process it. In this study, participants' accuracy in determining whether 60 health claims were true (e.g., "Vaccines prevent disease outbreaks") or false (e.g., "Vaccines cause disease outbreaks") was assessed. The 60 claims were related to three domains of health risk behavior (i.e., smoking, alcohol and vaccines). Claims were presented as Tweets or as simple text statements. We employed mouse tracking to measure reaction times, whether processing happens in discrete stages, and response uncertainty. We also examined whether health literacy was a moderating variable. The results indicate that information in statements and tweets is evaluated incrementally most of the time, but with overrides happening on some trials. Adequate health literacy scorers were equally certain when responding to tweets and statements, but they were more accurate when responding to tweets. Inadequate scorers were more confident on statements than on tweets but equally accurate on both. These results have important implications for understanding the underlying cognition needed to combat health misinformation online.