From a (2019) review on host susceptibility to influenza A virus (IAV):
Obesity was identified as a risk factor for IAV infection over a decade ago and confirmed during the swine flu pandemic [30, 31] when it was associated with an increased risk of death . Although comorbidities associated with obesity—specifically diabetes mellitus and cardiovascular disease—compromise pulmonary host defence and increase the chance of death following any severe systemic injury , an independent association between obesity and severe IAV is robust and replicated .
In parallel with the immune changes associated with pregnancy, obese patients are more likely to have impaired cell-mediated immunity and excessive chronic activation of the innate immune system . This is reflected in a study which demonstrated that among vaccinated adults, those who are obese are more likely to suffer severe consequences of IAV . Furthermore, it has been shown that obese adults have an impaired antibody response to IAV vaccination , and impaired CD4(+) and CD8(+) T cell responses IAV in vitro . Obese patients have a prolonged period of viral replication and shedding, even in the absence of clinical disease .
Some of these impaired immune responses in obese individuals might not be unique to IAV. Is anything else know in this regard, i.e. are there other diseases for which vaccines have been shown to be (somewhat) less effective in obese persons?