St. Pete is what folks calls the town, though they also call it the Sunshine City, as they claim they's no other place in the country where they's fewer days when Old Sol don't smile down on Mother Earth, and one of the newspapers gives away all their copies free every day when the sun don't shine. They claim to of only give them away some sixty-odd times in the last eleven years. Another nickname they have got for the town is "the Poor Man's Palm Beach," but I guess they's men that comes there that could borrow as much from the bank as some of the Willie boys over to the other Palm Beach.
It's from Ring Lardner's Golden Honeymoon, the short story published in 1922.
What does Willie boys mean and what does exactly the sentence mean?