Is being obese the unhealthy thing, or the lifestyle that leads to obesity?
Both? Being five foot and 200 pounds is going to be a problem regardless of
why one is that way.
How much does genetics have to do with getting fat?
A fair amount. Some people win the genetic lottery, and have an easy time being thin, tall, beautiful, intelligent, etc. But it's counterproductive to use the fact that some people have it easy as an excuse to create problems for yourself. if someone says "Bob is naturally thin, and I'm not. That's not fair, so I'm going to gorge myself on cheesy-poofs every day and never leave the couch!" he's only hurting himself.
A lot of factors contribute to health. Genetics is one factor, yes. Behavior is a factor, yes. Finance is a factor. If you buy cheap, unhealthy food because that's all you can afford, there are consequences to that regardless of how fair it is or isn't that those are your circumstances. And there's research that suggests that things like behavior, environment and diet can alter gene expression. So someone who grows up in an unhealthy environment, might have a more difficult time even if they make healthy decisions later in life.
But whether we say of someone who is fat that
"it's their fault" or
"it's not their fault" or
"well, it's kind of their fault, but they got unlucky and they really are trying to overcome problems that not everyone has" it doesn't change the fact that they're fat.