To find the experimental probability that the next customer at Burger Haven will want cheese on their burger, we use the formula for experimental probability:
\[ P(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}} \]
In this case, the number of favorable outcomes (customers who wanted cheese) is 2, and the total number of outcomes (total customers) is \(2 + 14 = 16\).
Now, we can calculate the probability:
\[ P(\text{cheese}) = \frac{2}{16} \]
This fraction can be simplified:
\[ P(\text{cheese}) = \frac{1}{8} \]
Thus, the experimental probability that the next customer will want cheese on their burger is:
\[ \boxed{\frac{1}{8}} \]