They should just change the size of the security gates to the width of the seats. If you can't get through security then they can't come on the plane
Interestingly, this is an approach which visitors to the Universal Studio (now defunct) ride of Duelling Dragons will be familiar with - my wife always reminds me of the sign which said 'guests of a certain size who are unable to sit in these seats, with the restraint in place and fully locked down, will not be permitted to ride, for reasons of safety to themselves and other riders.'
If folks would accept this for a fairground ride then its not entirely unreasonable to ask the same of an aircraft seat.