Well, the problem is not so much the fat itself as it is the consequences of the fat for your body.

For instance, at some point it may start and collect in your arteries, which is bad news if they ever get clogged to the point that no blood is flowing. This is called an infarction (which can happen anywhere in your body, not just the heart) and can cause tissue damage.

If this happens in, say, your leg, that may cause permanent pain as well as motor issues (as some of the muscle tissue that would be supplied by the blood vessel in question may die off as a result, thus restricting your movement), but if it happens in the heart, this can easily kill you.

Being overweight also causes all sorts of other complications, such as high blood pressure, shortness of breath, and increased risk of cancer, just to name a few. In general, there are all sorts of health risks associated with being overweight.