Because forgiving is centered in the moral virtue of mercy, you, as a forgiver, do have an interest in alleviating the other’s pain or even misery, caused in part by the unfair behavior. Thus, you are right that in forgiving you are “giving.” Yet, here is where I think your reasoning has a fallacy. You are thinking in “either/or” terms. By this I mean that you seem to be reasoning this way: Either I forgive or I seek fairness, but I do not do both. Under this circumstance, yes, you are right, to forgive is to be a giver who may not get anything back. Yet, I would urge you to think in “both/and” ways. As you forgive, then seek justice. In this way, you are both giving and seeking to right a wrong, or get something back that is important to you and possibly to your relationship with the other person. This balances forgiving and justice and thus you are not “stupid” when you forgive.
For additional information, see: Forgiveness: An Offshoot of Love.