I have a USA visitor's visa in my maiden surname. My new passport displays my married surname. I do not have my original marriage certificate with me but I do have a certified copy. Will this be sufficient proof of name change/ will they accept a certified copy?
No, it is not enough.
I have no idea why someone has not answered such a simple question yet.
You can no longer use that visa after your name change, even if you carry the original marriage certificate with you.
I changed my name. Is my U.S. visa with my old name still valid?
If your name has legally changed through marriage, divorce, or a court ordered name change, you will need to obtain a new passport. Once you have a new passport, the Department of State recommends that you apply for a new U.S. visa to make it easier for you to travel to and from the United States.
Also read this excellent Q & A on state.gov/libraries.