Earlier quoted context omitted.
Wary. I think the battle on this is already lost, but "weary" means tired, and is pronounced "weery"
FWIW Garner classifies this error as "stage 1" (rejected) in a recent edition, so we're still safe for a while, at least in professional writing. However, I do see this mistake more often than I see either word used correctly in non-professional Web writing, to include much work that is paid, but neither written nor edited at anything like a professional level. Garner attributes the error—among pros, anyway—to closen…
As a non-native speaker I'm afraid that some day I'll need a dictionary of homophones to decode written English.