Display day of week before date

This is already possible as the format that the dates are displayed in are taken from the settings for your blog, on the Settings->General page. Whatever you have set there is how the dates will be displayed. This is done so dates and times can be properly translated for other countries.

Please check out the PHP date page for the appropriate letter codes to format it exactly the way you want (using the custom option). You can find codes for PHP Date here:

http://php.net/manual/en/function.date.php

For example, if you wanted to display it as:
Monday, March 2, 2015
you need to enter:
l, F j, Y
in the Custom field for Date Format.
Note, after you enter something in the field, tab out of it, and the preview next to that field will update to show what it will look like.