I agree with the pp who said to serve something else with the pizza, like fruit or salad, carrot sticks, etc. If she does't want to eat those, you know she really is not hungry.
And remember, it takes more than 17 tries before a kid would accept food that they normally don't want to it. So don't give up. Set the veggies or fruit with the meal or as a snack and continue offering those even if she doesn't want them at first. At least you know she isn't really starving if she refuses the healthy food. But she will take them eventually if you keep offering.
I also agree that she may be thirsty instead of hungry. Even adults have a hard time with that and tend to eat when they are actually thirsty. My daughter kept complaining that she was hungry in between meals and even though she wasn't happy at first, she started drinking milk or water instead and she ate better at dinnertime.
Also, simple carbs like bread, crackers and cookies actually stimulate your appetite. So if she's getting that as a snack, it is not surprising that she gets hungry fast. If she can have nuts or dried fruit, that is also a good alternative. Soda also has lots of sugar and that may be stimulating her appetite as well if she is drinking soda with the pizza. Make sure there is plenty of fiber and protein in her meals. Beans and brown rice are filling, vegetable soups are good.
Also, it takes 20 mins for a person to fill full. So if she asks for more, ask her to wait a little for her stomach to digest the food and see if she is still hungry then.
Even 3 slices seem like a lot for a 6 yr old. I actually think one slice would be more appropriate and she can eat as much veggies or fruit as she wants. She won't be happy at first but you are the mom and you are ultimately responsible for those choices for her healths sake, whether she likes it or not.
Also, if she is overweight and hungry all the time, it might be time to get a physician's advice.