Cheng was particularly jealous of Dre and Mei Ying's relationship. Keep in mind of China's one-child policy and how there is a shortage of girls. Mei Ying might be the only girl that Cheng had a chance to marry.
In their first confrontation, Cheng gave Dre a black left eye. Dre's last blow the won the match landed over Cheng's left eye.
The scene where Dre falls asleep on Mr Han's lap and his following hesitation to put his hand on Dre's shoulder made a lot more sense when we find out about Mr Han's deceased son who would have been around the same age as Dre.
Dre asks Mei Ying to make a pinky swear. Notice that she looked offset when he holds out his pinky finger. It's because that's how you flip someone off in China.
This also gives Mei Ying's parents further reason to be pissed at Dre when he shows his pinky finger at the audition.
