I didn’t say it’s a priority just that it has to the attraction to her looks has to exist. not just that he won’t throw up looking at her. Of course her middos etc. are the most important criteria but attraction is also a necessary criteria. I remember a shmuz by a well known rosh yeshiva in my old yeshiva ( a very shtark one) where he cautioned guys from thinking that a ben torah shouldn’t worry about looks. he said that if he isn’t attracted to her he should not marry her.
I apologize for making you uncomfortable with the phrase “checking her out” but that is the most accurate way of describing it. I guess a different way to say it would be “seeing if you find her chitzonius attractive”