With the recent drive towards higher thermal efficiencies and lower emission levels in the power generation market, advanced cycle power plants have become an increasingly appealing option. Among these systems, humid air turbines have been previously identified as promising candidates to deliver high efficiency and power output with notably low overall system volume, weight and emissions footprint. This paper investigates the performance of an advanced humid air turbine power cycle and aims to identify the dependencies between key cycle design variables, thermal performance, weight and cost by means of a parametric design optimization approach. Designs of the main heat exchangers are generated, aiming to ascertain the relationship between their technology level and the total weight and acquisition cost of them. The research outcomes show that the recuperator and the intercooler are the two components with the largest influence on the thermal efficiency and the total cost. The total weight of the power system is driven by the technology level of the recuperator and the economizer. Finally, the effectiveness of the aftercooler seems to have the greatest impact in reducing the total acquisition cost of the system with minimum penalty on its thermal efficiency.