Mike, there are some websites which include actual scans of pages of some of these interesting contemporary magazines and newspapers, and I believe more and more are slowly being placed online for the benefit of researchers. I don't recall any of the issues of Harpers Weekly being placed online, but there are many others at certain web sites (e.g. SCIENTIFIC AMERICAN, which includes some very interesting data on the explosion aboard the USS CHENANGO, in April, 1864). The University of Michigan "MAKING OF AMERICA" web site includes several of these old magazines and books online, and are a great bonus for researchers. I think the alternate "MAKING OF AMERICA" web site from Cornell University also includes a number of these, and is slowly expanding. Some two or so years ago I also came across a web site that included actual pages of New York Civil War era newspapers, but cannot recall the exact URL. Also, due to the fact that a large number of Civil War era newspapers (including some from New York) are available at a University library close to where I live, I did not bother making a note of exactly where online I had seen it. As well I find navigating these newspapers on microfilm much easier than the online versions, so my preferences are in reading the microfilm versions at the University library.
However, I would not be surprised if similar scanned pages of Harpers Weekly is already online, somewhere.