I have the following example code:
<body>
<div id="a"></div>
<div id="b"></div>
</body>
If I add empty lines between each of my original lines, like this:
<body>
<div id="a"></div>
<div id="b"></div>
</body>
does that do anything to my site’s performance? Will the page load slower?
Yes, compact code speeds up page loading due to decreased payload…but not by a measurable amount, at least in most cases, unless your page is massive you won’t see a difference.
Pages should be delivered via gzip, making the size difference between spaced and un-spaced negligible, just do what’s readable to you, you’ll thank yourself later. As with everything, you have to weight the costs, in this case a very minor difference in payload size, with what’s easiest to maintain for you.