Taking a larger person up front to first class, space permitting, is much faster.
Otherwse the airline has to:
1. Identify the frequent flyer next in line to be upgraded,
2. Wait for him to gather his belongings and move up,
3. Move other passengers around so two seats* for the larger person are adjacent.
Fiendish idea that will never happen: Upgrade the larger person who is advised that his place in first class is tentative. When the seat belt sign goes off in flight, the frequent flyer next in line is identify and invited to orchestrate step #3 above and then take the first class seat. (Maybe offer the chance to the second and third in line if the first (and second) don't take up the offer.)
United has a preferred coach section called Economy Plus that passengers can upgrade to, in most cases for a fee. If there aren't enough regular coach seats, coach passengers are not summarily given empty first class seats but are given empty Economy Plus seats at no charge. On the other hand, United will try to upgrade as many eligible passengers as it can before asking for volunteers.
* Representing the larger passenger's original seat and the seat vacated by the frequent flyer who was upgraded.