Author Changes
In the midst of the Silver Age (around 1963), Charles Katz, Legacy Girl's original author, sadly passed away. He had been the author of most, if not all, of Legacy Girl's issues. Due to his passing, a new writer was hired - Robin Lowell, a man with ties to the growing counterculture movement. As a result, Legacy Girl's stories saw themselves aligning with counterculture ideals: instead of merely being a force for good on the homefront, she protests the Vietnam War. Her stories also see her fighting more explicitly for women's rights; she even gets a sidekick in the form of a young girl named Legacy Lass.
Origin
Legacy Girl's origin stays mostly the same, though this time, her predecessor Legacy Man is given a name: Robert Brand. He is a soldier who died during the Vietnam War in this age, though there is a short run of issues where he comes back to life with similar powers to Legacy Girl.
New Powers
Similar to Superman, Legacy Girl develops a whole host of new, wacky powers in the Silver Age. Some highlights include being able to shrink to the size of an ant, shapeshifting (but only in one issue), and creating shockwaves by clapping.
I would say Carolyn's most useful power in this age was her ability to share her superpowers with other people. This gave rise to a new sidekick of hers: Legacy Lass, AKA Mary Flint! Originating in Panorama #13, Mary was an activist and a fangirl of Legacy Girl's. She began helping Carolyn with investigations into shady dealings between businessmen with her above-average intelligence. When Legacy Girl found out who was helping her, she gave Mary part of her powers and a new outfit - letting her become Legacy Lass! The two would solve crimes and fight villains together for the remainder of the Silver Age.