。
I imagine a lot of people stress-eat.
Literal
Stress [with-で] binge-eating [obj-を] honorific-do-[polite-される] person [also-も] many [quot-と] think.
やけ食い (literally 'despair-eating') is a compound for 'binge eating out of stress or frustration' — where やけ (from 自棄 'desperation') + 食い 'eating' captures the 'eating out of frustration' sense specifically. ~される here is the sonkeigo (honorific) passive form, used as a polite way to speak of others' actions — not a true passive. 方 '(honorable) person / people.' A well-formed polite generalization.