WEST ORANGE, N.J.—When Deborah Nixon heads to her local pool in her swimsuit—a pair of long black leggings and a matching short-sleeved top like surfers wear—she gets compliments and admiring glances, at least from other women.

“It is the New Sexy,” says Ms. Nixon. The 58-year-old, who has abandoned her conventional one-piece bathing suit in favor of the more elaborate get-up, is convinced she looks and feels better with less of her showing.

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