What is a solution that has only a small amount of acid called?
It sort of depends on what you mean by "has a small amount of acid".......
If you mean "contains only a small number of moles of acid per unit volume of solution" then it is a "dilute acid".
If, however, you mean "contains an acid that only dissociates to a limited extent in aqueous solution" then it is a "weak acid".
You need to be careful when using terms like "strong" "weak" "dilute" and "concentrated" when referring to acids, and similarly you need to be clear on whether you are referring to the tendency to readily dissociate into hydrogen ions in water (strong/weak) or the number of moles dissolved per unit volume (concentrated/dilute).
Failure to be precise over such terms can lead to much confusion!