"at their expense"在這句即是"在他們的利益受損時"
用你比這句作例子:
"I will hold a larger portion of their sales, and I would be better off at their expense."
=>我會扣起較大的銷售額, (所以)我都會得益較多而他們的利益會受損...
比多一個例子你:
"Tom knows many of my strange actions. He tells these fanny actions to our friends and make me feel embarrassed. He is telling jokes at my expense."
除了"at one's expense"之外, "at the expense of (sb/sth)" 的意思都是一樣啊!!