When andrew proposes to heidi, her heartbeat quickens, her pupils dilate, and her breath quickens. Which nervous system divisions are activating these responses?

Sympathetic Nervous System is activated in this situation.

This branch of nervous system is associated with situations like anxiety, fear, danger, threat etc. So in such circumstances, it brings fight or flight response by activating adrenal gland.

Adrenal gland releases catecholamines which are adrenaline and noradrenaline which ultimately brings the appropriate physiological response.