“My daughter attends [high ranking Connecticut public school]. How much do colleges consider the strength of a high school?”
Unfortunately, probably not as much as you think. Plentiful exceptions abound so I realize that some admissions officials and some colleges account more heavily than others for the strength of an applicant’s high school. But many parents are delusional when they think that admissions officials can readily distinguish between Daniel Hand High School in Madison and Clinton High School in Clinton. The towns are neighbors on the Connecticut shoreline but the strength of the students at each is strikingly different. Admissions officials who grew up in other states would not know the differences.
Unless a college has created an input as part of its academic index algorithm that differentiates the two schools, then the relevant numbers used for the index (grades and test scores) are the dominant variables that formulate the all important cut-offs for which students will be evaluated for subjective factors (activities, essays etc.)
To be clear, certainly most East Coast college admissions officials would recognize that Bridgeport schools are different than most Fairfield County schools but the relative difference between Weston and Easton might not be as readily apparent. I do realize this can be disheartening to families that have paid a premium to live in towns with outstanding school systems. If there is any consolation, the competitive swimming pool that your children have attended will make them college-ready in better way than students from lesser schools.