A Mystery Solved!
I've seen similar stamps on building trim in Remington, Orange and Culpeper. Who the hell is Mesker & Bro? And how did they find their way from St. Louis, MO to Fredericksburg? Well here is the answer--

Frank and Bernard Mesker founded Mesker and Brother, a structural iron and sheet metal firm in 1879 based in St. Louis, MO. In 1880 they secured the commission for the sheet metal work on the St. Louis Art Museum. That was followed by work on the St. Louis Exposition building. In 1884 Mesker & Bro. purchased a sheet metal company in Washington, DC that was going out of business. The company had 1500 catalogs depicting its sheet metal products. Frank Mesker decided to replace the covers of the catalogs with Mesker Brothers covers and send them to potential customers in surrounding territories. The effort led to a large number of mail orders and the company began publishing its own catalog the following year. The new catalog depicted the new sheet metal storefronts the company began producing in 1884. During WWI the company produced field stoves for the army. In WWII they produces parts for subs. Mesker & Brother was sold in 1961.