Set the width of the select box in Drupal form
The size attribute you are trying to set there is related to how many items are shown at one time. So in those terms the height would increase and it would show a scrolling list of items to choose from if you added size to the select box. See Form API Docs for more information.

You need to target the select box with CSS to change the width (most themes/browsers set the width of a select box to width: auto; so it would be as long as the longest item to be selected). 

So for instance if you want to set all of your select elements to take up the entire width of their containing divs you would set:

select {
  width: 100%;
}


Or if you want to target all select elements with a class of .form-select you could use:

select.form-select {
  width: 50em;
}


You can use id's also like select#id-of-element but using a class is the more generally accepted best practice for styling (not just in Drupal but general FED practices also).