Yes it is possible, this is what the ranking panel is for.
Be sure to have imported your "weight" values as numerical values (Float, Integer, Long...), not textual (String). This can be checked in the import wizzard, at the step when you are asked to confirm / choose the type of each attribute.
Once you have made this check, visit the "ranking" panel in Gephi and select your weight attribute in the drop down menu. Then click on "Apply".
This tutorial has some slides on ranking, and more: http://www.slideshare.net/gephi/gephi-quick-start.