Leery implies a negative feeling towards something, hinting at doubt or distrust, not just caution. He gave a leery glance at the suspicious offer.
Pro Tip 2/3
Intensity of Mistrust
Leery suggests a moderate level of suspicion, not as intense as paranoia but more than just being careful. She's leery of emails asking for personal information.
Pro Tip 3/3
Past Experience
Use leery when past experiences influence someone's current hesitancy or suspicion towards someone or something. Burned by past investments, he was leery of new financial ventures.