It's too bad
Mike doesn't have room to give references as to where he takes his meanings from. The reference books I have which I think of as being more reliable on Biblical names all simply list the meaning of
Delilah as "unknown".
However, I'm not sure that "delicate" and "languishing" are that far apart in meaning. I certainly can imagine the ancient Hebrews having a word which encompassed both of those concepts together.
As for its popularity in the USA -- just read the comments under the entry for
Delilah on this site, and you will find the reasoning of many people who think
Delilah is a pretty name and who believe the Biblical character gets a "bad rap" and actually should be seen as a good role model for a strong, resourceful woman. Not sure I'd agree with those sentiments myself, but they seem to be common. :)