Why were David's eyes in tears when he was off-loading the cargo of black goo?

This question is one of the most intriguing ones, as it suggests an emotional connection and hints at his love for Elizabeth Shaw. Why else would he cry? Who else would he cry for? Shaw died in the spaceship during their journey from LV-224 to Planet 4. David was cared for by Shaw, and his love for her grew to a level where she became the only person he loved, while the rest of the world meant nothing to him. Shaw's death resulted from wounds she sustained during surgery, likely due to a lack of appropriate medicines on the Engineer's spaceship or possibly an infection that eventually took her life. The root cause, of course, was the Black goo invented by the Engineers. Consequently, the Engineers appear as enemies to David, the cause of the loss of the one he loved unconditionally.

Planet 4 was never the home planet of the Engineers; it was just another planet where the Engineers seeded life, similar to what they did on Earth. The humanoids on that planet welcomed the Engineers' spaceship as if greeting gods, viewing them as divine beings to be worshiped.

When David and Shaw boarded the Engineers' ship in Prometheus, they chose the same destination, presumably pre-set in their system, assuming Planet-4 was the Engineers' home planet.

David unleashed the Black goo, killing all the Engineers in his vengeance and carrying the weight of his loss with tears in his eyes.

After settling on Planet-4, the lonely David attempted to revive Shaw in various ways, possibly using the black goo or attempting to create a bio-mechanical version of her. The dissected and disfigured body of Shaw we saw was the result of several failed attempts by David.

The crucial point is that David never killed Shaw. It would have been impossible for him to do so. His remarks to Daniels about what he did to Shaw were merely satirical.

After losing Shaw, David became fascinated with 'creation' and sought to create the perfect organism. Following Shaw's death, other humans meant nothing to him, and this marked the birth of the villain within him.