This paper presents a multiple weight set weighted random BIST scheme to perform power aware test which takes into account peak power constraint and reducing the number of required weight sets. Exceeding the peak power budget during test provokes problems such as erroneous circuit function due to IR drop and electrical damage to the circuit. However, excessive power reduction during test can degrade fault screening capability of the test since the test environment becomes substantially less stringent than the environment in which the device is actually used. Therefore, controlling power consumption during test operation is important to perform adequate testing. In this paper we address both these problem simultaneously. The main contribution of this paper is to provide an efficient scan based weighted random BIST scheme within power constrain. We assume full scan environment, test per scan testing, and single stuck-at fault model. Genetic algorithm (GA) based optimization method is proposed to find effective weight sets.