Re: critical illness
The insurance coverage is applicable unless there is a rider with the policy that specifies the exceptions.
There maybe a denial to issue a policy based on some risk factors, but those disqualifying factors should/would have been disclosed with the insured's application. Acceptance indicates approval to the terms of the contract. If obesity was not a medical issue considered by the insurer prior to a condition, it can't decide later to make it an exception; however, with a renewal and acceptance by the insured there can and often are policy changes.