Why do people often say 最多 in Cantonese when they mean "at the very least"? I often hear on TVB shows that people say 最多 in a context when they mean to say, "at the very least?" For instance, something like, "At the very least, I'll take you to dinner tomorrow for being late."

Why is this?
Consider it this way: If your offer and his expectation from you are at two opposite ends, then the most you can offer only meets the least he has expected, or even less.

So the perspective(point of view) affects the use of "most" and "least" -- quite subtle. To make a specific case clear, we need the vivid context.