The menu height can be changed through the Menu general editor. First drag and drop a menu widget. Then, hover over the widget and click on the pencil icon. Next, click on the advanced tab. Finally, click on Menu and general and move the slider to the left and right or type in the desired pixel height. 

Optional: Check the box fit subitem to width in order to have the sub buttons be the same size as the main buttons.

Here is how to change the menu height:

Step 1: Get into advanced mode (See Menu Widget - Advanced). 

Step 2: Click on general tab (A). 

Step 3: Adjust the height (B). 

Note: The menu height only affects the height of the container.

Tip:  Make sure height of the container is big enough for buttons and sub buttons radius.