This is the 14930th most frequent Russian word.
поддерживая
"Supporting" or "maintaining."
Here, 'поддерживая' indicates the simultaneous action of her supporting the child physically as she walked.
Она шла медленно, поддерживая ребенка за руку.
She walked slowly while holding the child's hand.
The word “поддерживая” explains the manner in which the action (speaking) was performed, indicating he supported his viewpoint during the process.
Он говорил, поддерживая свою точку зрения.
He spoke while supporting his point of view.
'Поддерживая' emphasizes the continuity or presence of an open dialogue during the meeting.