is what is needed here. It's not fair to deal with it on an ad-hoc basis when there is a complaint. Don't put other passengers in a position of having to complain, and don't put obese folks in the position of having to be embarrassed by a complaint.
An objective size limit needs to be conveyed at the time of purchase — just like for baggage. Then there are no surprises when you get to the airport and you're asked to pay more if you're found to be in excess of those limits. The policy alone might be enough to curb the issue if people know it might come up — without having to go to the expense of actually weighing passengers during boarding or check in. That's a logistical thing I'd just as soon not have to deal with as a society, but if it became necessary, there is a way to implement it that respects privacy and avoid public embarrassment. A scale that you can stand on at check in that doesn't give a number, just a red light/green light indicator oriented in such a way that only the person on the scale can reasonably see it, would go a long way. People on the edge can validate well before getting to the boarding gate and having the potential anxiety or embarrassment.
Frankly, I'd rather we as a society just invest in addressing the obesity problem itself, instead figuring out ways to deal with the challenges it creates, but we as a people seem to be struggling to have an objective discussion about that these days.