The property of being leery, suspiciousness, distrustfulness.(noun)
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Use "leeriness" in a sentence
"For starters, the constant leeriness towards women, the assumption that any vaguely attractive woman was nothing more than mattress-fodder, makes even yours truly - no fan of political correctness - feel uneasy."
"One of Mr. Rodriguez's biggest gripes has been institutional clients 'leeriness about the high cash level his stock fund maintains."
"Obama's uplifting moment followed an by his former opponent when she did her best to further bridge the divide between those Democrats who express leeriness about Obama."