Excessive weight is connected with an increased risk of certain life-threatening diseases. However, some evidence shows that among patients with chronic diseases such as heart failure (HF) chronic kidney disease (CKD) and COPD, increased weight is paradoxically associated with a decreased risk of mortality. This counterintuitive phenomenon is referred to as the obesity paradox. The obesity paradox has been mostly observed among certain cohorts of patients with HF, but not specific to patients in the Intensive Care Unit (ICU) setting. This paper studies the relationship between obesity and mortality of ICU patients with and without HF and presents evidence supporting the existence of this paradox. The results provide helpful insights for developing more patient-centric care in ICUs. Additionally, we use both the MIMIC-II and (recently available) MIMIC-III databases, for which few comparative studies exist to date. We demonstrate an aspect of consistency between the databases, providing a significant step towards validating the use of the newly announced MIMIC-III in broader studies.