How much weight can you lose by eating no processed foods

It depends on your body and fat / muscle percentage. 

The answer depends entirely on the bodyweight you start off at, the amount of processed foods you were originally eating, your age, your body-mass index (which measures how much of your weight is from fat and how much is from muscle), and how active you are. 

But here's one scenario. Imagine you drink three 12-ounce Coca-Colas each day. They have about 140 calories each, all coming from highly processed sugars. If you stop drinking those sodas altogether, you'd cut almost 3,000 calories per week from your diet, or 12,000 calories per month. To lose one pound of body fat you have to cut about 3,000 calories from your diet, so you could lose 4 pounds per month simply by choosing not to drink those three daily sodas.