Timestamps aren't meant for most users
Showing friendly names such as
2 hours ago or
yesterday can quickly provide context to the user as opposed to showing them
2015-01-27 18:54:03.259 Mixing both formats together will always cause friction (anything that forces a user to ask a question in their mind adds to cognitive friction). In almost all cases mixing them will do more harm than good so leave off the day of week. Even at the expense of providing context, there should be no question that what I'm looking at is a timestamp.
While friendly date formats are better displayed in the UI by default, timestamps should be hidden until a user requests it (such as hovering the mouse over a displayed date/time or changing a setting)
Friendly names such as the ones used in Outlook provide better context than
Friday. The names for each day of the week loses context every 7 days. Saying
Tuesday today might help a little but saying
Tuesday next week would be confusing even without bringing timestamp in to the mix...