95b323b7_of_Size__Policies___Yahoo_News__Stated_policy
[Airline] United [Costs] A second seat may be purchased for the same fare as the original seat provided it is purchased at the same time those who do not risk being charged walk-up fares later on. No. [Stated policy] 
If you cannot demonstrate that the armrests can go down and stay down regardless if you are seated next to a friend or family member you must purchase a second seat. Those who decline to do so or upgrade to larger seats risk being refused at the gate.
Airline "Customer of Size" Policies - Yahoo News
Stated policy