Read the help section called Genericons – Add Icons to Your Content
It gives you all the info.
Once you have copied the HTML from the genericon site that correspond to your icon, just paste it in front pf your menu label in Appearance > Menus. You do need to have created your menu with WordPress Custom Menu
As a rule (and specifically Weaver Xtreme Plus’s implementation), a Mega Menu will always be a pulldown, and not an item on the main menu bar. @scrambler ‘s answer is the way to add icons to menu items.