Weary and wary are easily confused words.
The spell-check application of most word processing software programs would not catch a slip-up of these two words. Spell-check is looking for words that aren’t in its dictionary, and words that resemble words in its dictionary, but are possibly spelled wrong. Spell-check isn’t perfect. It doesn’t know and can’t guess what word you wanted, or what word you meant, it can only judge the words on the page. If you used words that are all spelled correctly, it gives you a pass anyway.
Autocorrect suggests words that start with the same letters. It’s suggesting what word you may want to save time, but quite often, its suggestions are pretty off base. They don’t help you out, but they do make you laugh.
Weary (pronounced “weer-ree”) has multiple forms.
As an adjective. It describes a person who is fatigued or tired by circumstances. This can be physical fatigue, emotional tiredness, or both.
As a verb, it means to fatigue or tire, to exhaust or wear out.
Wary (pronounced “where-ree”) is an adjective. It describes someone who is cautious or timid in their dealings. Perhaps they’ve been burned before. Perhaps they anticipate bad outcomes, poor treatment, or other negative occurrences.
The following story uses both words correctly:
Warner originally wanted to run a charity marathon with friends, but now he was wary of being unable to finish the race. A recent bout with Lyme disease had really made even the thought of overexertion made him feel weary.