This is the 10333rd most frequent Polish word.
chwilami
"Chwilami" means "at times" or "occasionally" in English.
Here, 'chwilami' is used to express occasional or infrequent incidence of feeling tired.
Chwilami czuję się bardzo zmęczony.
At times, I feel very tired.
'Chwilami' in this sentence emphasizes particular moments within the discussion when the person appeared convincing.
Podczas dyskusji, chwilami brzmiałeś bardzo przekonująco.
During the discussion, at moments you sounded very convincing.
This use of 'chwilami' indicates specific and identifiable moments of expressed interest.