Yes, it can be normal to cry a lot during a psychedelic session. Strong feelings often come up, and tears are a common response.
Experiences tend to move in waves: sadness may rise, be felt, and settle, making space for calm, relief, acceptance, gratitude, or even joy. Crying can be a natural release rather than a sign that the whole session is negative.
If it happens, allow it with curiosity. Breathe slowly, ground in your body, and use simple comforts like a blanket or tissues. If it feels too much, you can pause, open your eyes, change posture, or ask a trusted sitter or facilitator for support. For a short take on why sadness can arise and how to relate to it, see this discussion.
Be gentle with yourself and let whatever comes move through. Take care.