I haven't rewatched Prometheus for a while now, so I'm a little hazy. But wasn't David always slinking off to receive "orders" from the sleeping/dreaming Weyland for most of the movie?
When Weyland dies, presumably David is no longer "owned" by his primary user Weyland. Whether or not that means David is then even more/less of a loose cannon who knows.
His gesture towards Shaw (seemingly helpful) to find a spare ship - thats the first time we see David without Weyland's influence, right?