To find the total change in William's weight over the four weeks, we can add up the pounds he lost or gained each week.

1. First week: Lost 4 pounds → $-4$ pounds
2. Second week: Lost 7 pounds → $-7$ pounds
3. Third week: Gained 4 pounds → $+4$ pounds
4. Fourth week: Lost 2 pounds → $-2$ pounds

Now, let's sum these changes:

$-4 + (-7) + 4 + (-2) = -4 - 7 + 4 - 2 = -9 \text{ pounds}$

So, the total change in William's weight over the four weeks is a loss of 9 pounds.

Would you like more details or have any questions? Here are five related questions that might interest you:

1. How would the total change be affected if William gained 2 pounds in the fourth week instead of losing 2 pounds?
2. What was William's net weight change after the first two weeks?
3. If William wants to lose 5 more pounds, what should his net weight change be in the following week?
4. How can we calculate the average weekly weight change for William over these four weeks?
5. What would be the total weight change if William lost 3 pounds in each of the four weeks?

Tip: When solving problems involving changes in quantity, consider using a number line to visually track increases and decreases.