This is the 14827th most frequent Russian word.
поболеть
"Поболеть" means "to be sick for a short time" or "to support/cheer for (a team)."
Here, 'поболеть' means 'to cheer' or 'to support enthusiastically'.
Я хочу немного поболеть за свою любимую команду.
I want to cheer a bit for my favorite team.
Here, 'поболеть' is used colloquially to mean 'to pretend being ill' to justify getting a leave.
Он решил поболеть на некоторое время и взять отпуск.
He decided to be ill for a while and take a leave.
Here, 'поболел' means 'to be ill for some time' and describes the person's recent recovery.