People get pear shaped. This is the mostly likely reason that "pear shaped" may mean that everything's going wrong. (Unless, of course, you think that gaining a fat bottom and chunky thighs is a cause of celebration*.)When things go pear shaped, everything sinks down. It happens, and there's little or nothing you can do about it. No cosmic StairMaster will solve the chaos.

I seriously doubt that the slang usage came from planes or balloons or pear drops**.

* though, if you are putting on weight, being pear shaped is seen to be healthier than becoming apple shaped. Less of a risk of heart disease.

** though, if your coffee smells of pear drops please don't drink it. Someone's trying to poison you. Or has spilt their nail varnish into it, at best.