Higher levels of body fat (which is almost always the cause of a high BMI unless you are an active athlete) is pretty directly tied to inflammation and pre-diabetic insulin resistance. This subsequently results in the liver producing more triglycerides and lipoproteins that clog the circulatory system and the inflammation itself promotes hypertension. All of this together results in more heart attacks and strokes. There's a pretty clear mechanistic link between obesity and cardiovascular disease.

That doesn't mean obese people are "to blame" for any medical complications they might suffer from obesity. It also doesn't mean that obesity is a death sentence; people's bodies function differently and we've all heard stories of pack a day smokers that lived into their 90s. But there is absolutely a connection between the two.