If you want a logo image and a menu side by side, given you have plus, the easiest and what will give you the most control, is to use the header widget area with two widgets, put the image in the left one, and an Extra menu shortcode in the right one.
Then you can use the settings of the header widget area, to either split the space 50/50 with two columns on desktop and small tablets and let them stack on phones, or you can use the custom widget width settings (as explained below) to set a different split % for the image and the menu, and decide what that will be on small tablet and phone using the custom widget width boxes for each device.
http://forum.weavertheme.com/discussion/10342/weaver-xtreme-tips-and-tutorials-part-1#Item_1
Once in place we can help fine tune