Why did Beerus say "Say something." at the end of Episode 118 of Dragon Ball Super? At the end of Episode 118 of Dragon Ball Super, just after Champa and Universe 6 is erased, Beerus says "Say something."

Could this mean that Champa will continue to live on in Beerus' mind? Or did they previously have a connection that allowed them to communicate telepathically?
Due to their brotherly bond, he wished to have heard some goodbye words. Beerus deeply cares for Champa as does Champa for him. They are like siblings. They always fight, cause drama but at the end of the day they want the best for each other.

During the fight between the Namekians and Gohan &amp; Picollo. Whiz was asking Beerus why he was silent for a while and is he worried that Champa's universe might be erased. Nobody knows Beerus like Whiz does, so if he asked that question then it implies that Beerus was genuinely worried about Champa.

Remember the episode of the tournament before this where Beerus's universe won from Champa's universe? They were awarded a wish with the universal Shenron. What did Beerus wish for? To restore the planet earth in Champa's universe, so that Champa could enjoy the good food as well. He could wish for selfish things or to strengthen his warriors or whatever else, but he did it so that his kid brother could be happy and enjoy the food as well. This indicates that Beerus cares about Champa the same way as an adult brother cares for his kid brother.

So back to the universal tournament; the stakes are high and while they enjoy fighting each other we can conclude that both want to win, but they don't want their brother to lose either. If anything Champa wishes deeply that if he doesn't win then his Brother Beerus should and vice versa. 

At the final moment Champa called out to his big bro and would've probably said something but he isn't a fool. Due to his troubled face he resorted to making a funny face instead, indirectly telling Beerus to not worry and rather to focus on winning. Beerus on the other hand... wanted to hear some parting words. A "good bye!" or "good luck!" would have lifted his spirits a bit, but knowing Champa he didn't want to resort to a touching goodbye, so he acted accordingly to his behaviour. Beerus wish to hear some final words was what made him say that. 

This is simply the bond of an elder brother losing his younger brother while both are aware that one is going to vanish... and at the moment of vanishing you would want to hear your brothers voice doesn't matter what it is. This is more something emotional and sensitive rather than some beyond-human-level form of communication. This was the feeling of losing someone close to you while being unable to do anything about it at all. 

Off-topic; Vegeta was pretty pissed about it as well. And remember what Vegeta said to Cabba? He would win the tournament and wish Cabba's universe back so that Cabba could show him around in his universe. At the current episode and ending I think that Beerus has a similar feeling right now. He wished planet earth back for his brother previously. It is quite obvious what his next wish will be (if they are granted a wish at all).