Balloon currently syncs three things with Apple Health:
Steps - read only
Fiber - read and write
Mood (State of Mind) - read and write
You can set up the connection from the Health app on your iPhone:
Open the Health app
Tap the Sharing tab
Scroll down and tap Apps
Find Balloon in the list
Turn on the data types you want to share (Steps, Fiber, State of Mind, etc.)
Make sure both "read" and "write" permissions are enabled for any data you want to sync both ways.
Note: Balloon will only appear in the Health app's list after you've granted it at least one permission. If you haven't yet authorized anything, it won't show up there.