Hello Sham,

Send us a pic please, that will be a good starting point.
From your description I would guess that it has a pronounced "smile" shape to the edge of the blade. But your description also suggests a severe rounding to the edge. I have seen that before on W&B wedge type razors.
I think both of the suggested explanations may have merit... a very slack strop and/or the razor was sharpened like a knife with the spine raised off the hone. In either case the solution is the recreation of the bevel which will require a lot of work.

But...send a pic please.