I know Juno claimed him as her champion when he was born and stuff, but I do wonder if a part of what endears Jason to her is that he isn't one of Zeus/Jupiter's favorites.
She probably has a big inferiority complex directly caused by Zeus cheating her. Not helped by Zeus keeping his gloating mistresses Leetoe & Smelly in her sight on Olympus and openly favoring their sons to hers.
But Jason Grace is not one of the sons he favors. Despite his power, this boy is no Hercules, he's not lucky enough to be that loved.
Maybe she sees her own children's pain in him... Ares never being able to make Zeus proud no matter what he does, Zeus being a major asshole to Hephaestus when he opposes Zeus to do the right thing, Hera's daughters never receiving the same love from Zeus that Athena and Artemis do (if he remembers them at all).
Obviously Jason's case is made worse by Beryl being... not a good mom.
Remember that Hera is the same woman who acted motherly to Heracles after he was rejected by his mother (not blaming Alcmene btw, Heracles was a product of her rape) before realizing he was one of her husbands favored bastards (who he planned to make king of HER patron city).
She has a soft spot for children like Jason.