Dictionary lookup wider and taller (pop-up dictionary lookup styling) in OS X
First of all, find out dictionary path you want to modify. This is dependent on the dictionary you want to modify, but you path should look something like this:

/System/Library/Assets/com_apple_MobileAsset_DictionaryServi‌​ces_dictionaryOSX/04‌​2bf65b3ae80e4564c339‌​fcf00fa9924bd16dd3.a‌​sset/AssetData/Apple Dictionary.dictionary/Contents/Resources/English.lproj/Apple‌​Dictionary.css


Then open this file in any text/code editor you'd like, it could be even vim, like in the original question, and open it for modification, search for font-size parameter for body element, it could be defined in pt, px, em. If you want to deep into CSS details, you may read up tutorials or manual on the font-size. It appears to be regular CSS file, for definition of styles, so it's easy to work with it.

You may change the font-size, to make it bigger/smaller, it could achieved by modification of parameters in CSS:

body {
  ...
  font-size: 15pt; /* &lt;== look for this parameter, and scale it up to your taste */
  ...
}


Or like this: 

html.apple_client-panel body {
    ...
    font-size: 15px;
    ...
}


You may find some screenshots and additional explanation on apple.disscussions.

One also can play with line-height, if font-size haven't brought enough readability. If you want to change the window itself or spacing around text, then you may want to modify margin (margin-top, margin-bottom, etc) or padding (padding-left, padding-right, etc). 

Tried to explain this to the guys, who are not web-developers themselves, hope this helps. Ask if you gotten additional questions to me, or search them on StackOverflow (it's for developers questions), but I think it will be straight-forward for you now.