For context: the name is Billie (my dad died when I was younger, his name was William, but I wouldn't consider it if I didn't like the name).

I actually completely agree with you on the nickname thing (though more in general than for a specific gender), this is just one of my only exceptions.

It doesn't seem too cutesy to me, but then I know adults of both genders with the name so most of my associations are strong adults (women in particular). It feels more like the name Sadie to me than Charlie (maybe because Charlie is an obvious cutesy shortening of Charles/Charlotte, while Sadie and Billie are distanced from their original forms).

But again, I'm not in the US so the name might have a totally different vibe over there (so I wouldn't be offended if it did fall into the negative category for you). I know names with -ee sound endings do sound more cutesy in an American accent than a Scottish one. With the Billie spelling it's almost exclusively feminine in my country whereas the Billy spelling is almost exclusively male (and Billy is used a bit more frequently as a full name for men than Billie is for girls, though still less common than its use as a nickname for William, so it's not a case of men get the strong name while girls get the nickname).