Billy trying to kill Stu
For anyone who loves this movie, I recommend listening to The Rewatchables podcast on TheRinger.com. They break down this entire movie and its really well done.
One thing they pointed out that I had never thought of before, but makes perfect sense... Billy was trying to kill Stu when they were "fake" stabbing each other. The way he was acting while doing it, and where he was stabbing Stu would indicate he wanted him dead. Also Stu talked to much and was a little to proud of the murders, and after Sydney and her father were dead, then Stu had no one left to kill and Stu would have out lived his usefulness. Why keep him around as a loose end.