Why does Dill feel sick in the courtroom?

Because of how Tom Robinson is treated.

Dill, like Scout and Jem, is horrified at what is taking place the court. The brash injustice, ignorance and bigotry of the jury (and many of the citizens of Maycomb) is too much to handle.

The injustice of the trial disturbs him.

Dill feels sick in the courtroom because of the way mr Gilmer-the circuit lawyer representing Mayella Ewell treats Tom Robinson.

When Mr Gilmer cross examines Tom he addresses him as 'boy', saying to him also 'Were you so scared that she'd hurt you, you ran, a big buck like you?'

Directly after Atticus cross-examined Mayella, adressing her with 'ma'am' and 'Miss Mayella'. The juxtaposition of the conduct in which both these lawyers used makes it clear a daylight to Dill how unfair the blacks are treated and prejudiced against, shown no dignity whatsoever. To a child this is more evident and not made to be pushed to the side and forgotten about it.

Dill reacts to it the only way he can by crying, when Dill moves outside to calm down he says to scout, 'That old Mr Gilmer doin' him thataway, talking so hateful to him-' this so evidently shows Dill knows the injustice that goes on. After the verdict that Tom is guilty Atticus says, 'They've done it before and they did it tonight and they'll do it again and when they do it-seems only children will weep.' As Atticus can be seen as Harper Lee's spokesperson in the novel for morals, this could imply that she knows only children because of their naivety see real injustice because they do not try to bury it like the town of Maycombdo so well. Dill's tears symbolise INJUSTICE.