I have not read all the responses to you query to see if someone might have sent this information. If your Charles was born in 1813, he would have been very old at the time he lived in this area. Anyway I will submit it as a possibility.
In the book "Arlington Heritage" Vignettes of a Virginia County by Eleanor Lee Templeman, page 138 - "The Doubleday Mansion Mystery." ..."The builders, Colonel Charles William Doubleday and his wife, Sarah Louise. They built in 1898 and departed eighteen years later. they were obviously wealthy and cultured and are said to have entertained notables of Washington and cavalry officers of Fort Myer. their virginia neighbors did not know them personally and are unable to tell me who they were, from whence they came, why they left such beauty, where they went, and whether or not they had heirs."
The home is at 2301 North Uhle Street, on the promontory of the Potomac Palisades between Spout Run and the Potomac River. It can be seen from Key Bridge.
The author mentions wondering if there was a relationship to General Abner Doubleday, the "father" of baseball. She states this couple is unknown to the Doubleday family of the publishing company.