This paper investigates the impact of weighting techniques combined with Grey Rational Analysis (GRA) when Multi-Attribute Decision Making (MADM) techniques are applied to wireless network vertical handover. The performance of the GRA algorithm is investigated with Analytical Hierarchy Process (AHP), Fuzzy AHP, Analytic Network Process (ANP), Random Weighting (RW) and Least Square weighting (LSW) techniques for background, conversational, interactive, streaming classes of services. It is observed that the use of different weighting techniques for every traffic class results in widely varying performance in terms of percentage of network selection and ranking abnormalities. It is therefore concluded that when GRA is applied to vertical network handover, careful matching among different traffic classes and proper weighting techniques should be performed in order to optimize performance in terms of judicious selection of the best network with minimal ranking abnormality.