Real quick, I wanted to share a theory about Covenant (or whatever it's called when it comes out)...
David was given orders by Weyland to "try harder", and he will never stop trying to carry them out, because Weyland is dead and no one can countermand his order. He's using the technology he found to try to solve problems Weyland asked him to, which doesn't always take you in a straight line, so he's just experimenting and improvising... and we don't really know what his orders were...
Using the technology in the Engineer's ship, he transmitted his consciousness (or just the data he had) back to Weyland on Earth/Mars along with his plans and details about what he had already done. They either just used that data to plan the mission, or they also loaded his consciousness into another David on Earth/Mars (the one looking out the window in the trailer). This David can be updated with new information from the David in the other part of the universe via more transmissions...
This David knows more about alien technology than anyone ever, and he is under no obligation to share that information with anyone outside of Weyland. He's probably CEO or at least an MVP. This is how Weyland/Yutani becomes "The Company" which dominates the future, because who could compete? He's the best, most capable, most dedicated corporate espionage agent ever...
Also, although Weyland is dead, he did die on a ship built by superadvanced bioengineers, and his body was still there the last time we saw it... it's possible that with nothing but time our supersmart android friend has rebuilt a new Weyland... or rebuilt the other humans whose dna he had... and experimented on them before Covenant arrives...
