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.
Show friendly dates and times as needed, timestamps when requested
Depending on the situation timestamps should always be hidden until a user requests it (such as hovering the mouse over a displayed date/time)