Virgo started collecting science data during weekends in order to not interfere with commissioning activities. The goal of Weekly Science Runs is to ease the transition between commissioning periods and data taking periods, in addition to providing data sets exploiting the stationary behavior of the detector. The detection of gravitational wave (GW) bursts emitted by core collapse of supernovae is one of the most difficult tasks for the GW community due to the fact that there are uncertainties in the exact shape of the waveforms, as we do not have complete models. A major task for this kind of detection effort is the cleaning of the event triggers found by the detection pipelines, namely the removal of accidental transient signals due to noise source events. In order to clean our data from false GW events, we need to define a strategy for data quality cut and veto of auxiliary and environmental monitoring channels. In this paper we report on the analysis we performed on data acquired during Weekly Science Runs to explore and define the data quality cut and veto studies for burst analysis.