The histogram is built from the entire image. Unless the gray card fills 100% of the screen, you should expect to see all sorts of other stuff represented there.
Indeed, if it's only a linear 50% of the frame that you're filling the gray card with, the area that covers is much less than 50%....
But, if you're using a gray card as you describe, the histogram is pretty irrelevant unless you're watching against clipping of especially bright highlights...in which case, the meter reading off the gray card becomes irrelevant.
You might also consider a handheld light meter instead of a gray card. Logically, they function the same way, but the gray card has disadvantages -- not the least of which is that even the low levels of gloss on a gray card can wreak havoc with your camera's meter readings. Try it -- step outside on a sunny day, stand in a single spot with the Sun at your back, hold the card at arm's length, and rotate the card. See how much its brightness changes, even to your eye, depending on whether or not it's pointing near or away from the Sun! Now, which of those angles is the "right" one for setting exposure?
A meter doesn't have those problems, due to its design. Stand in the place of your subject (or as close as you can get), aim the dome at the camera, press the button, and you've got your exposure.