You can't change the height of the br tag itself, as it's not an element that takes up space in the page. It's just an instruction to create a new line.
You can change the line height using the line-height style. That will change the distance between the text blocks that you have separated by empty lines, but natually also the distance between lines in a text block.
For completeness: Text blocks in HTML is usually done using the p tag around text blocks. That way you can control the line height inside the p tag, and also the spacing between the p tags.