From Longman Dictionary of Contemporary Englishkeep a weather eye on somethingkeep a weather eye on somethingWATCHto watch a situation carefully so that you notice anything unusual or unpleasant Keep a weather eye on your finances. → weather
Examples from the Corpus
keep a weather eye on something• They dabble in composites, and keep a weather eye on the developments made by the small specialists.• Both, for different reasons, kept weather eyes on the cloning work.• This lets you keep a weather eye on your finances. 