Have you tried the spiritual gifts test? It could help make sense of this calling.
My father had it too. He was a tough man, but he wept in every conversation about Christ. He could see the world’s suffering through God’s eyes.
The church has discussed this for over 1,500 years. In the 3rd and 4th centuries, monks like Evagrius of Pontus wrote extensively about what they called ‘the gift of tears’ (donum lacrimarum).
They saw it as a unique spiritual blessing, different from ordinary emotional reactions.
Your body is responding physiologically to feeling completely safe. Prayer is probably the one part of your day when your body moves into rest mode. So don’t fight it.