Correct. Obesity generally impairs the function of the immune system and even access to some stored nutrients like vitamin d, but here is a catch. There can be two obese persons, but one can be healthy with a properly working immune system, and the other one unhealthy with a dysfunctional one. One can be insulin resistant and on its way to diabetes, the other can have functional fat stores, which does not significantly impact health, even if they appear to be on the fluffier side.