The amount of weight you lose for not eating for 1 full week would depend on how much you currently weigh.
If you feel into the "obese category" instead of just "overweight" you'd be able to lose more weight as you'd be more easily able to create a large caloric deficit from not eating...
Your body requires a certain amount of calories to maintain it's current
weight (body weight in lbs x 15)...so if you were 150 pounds, that would be
150x15 = 2,250 calories/day.
To lose 1 pound you need to be in a deficit of 3,500 calories. So if
you ate 500 calories less than this 2,250 each day (1,750 cals/day) you would
lose 1 pound each week.
Again, if you were heavier, you'd create a greater daily deficit and lose more weight.
Also, this isn't taking into consideration the water weight you will lose, which could be 3-5 extra pounds.
But...this really isn't healthy and I would strongly recommend you not go any lower than 1,200 calories/day.
Your best bet is to find a proper diet/exercise routine and follow it to a "T for better results.