We've actually taken our children on three cruises, and have stayed in balcony cabins each time...
I'm pretty sure the doors are the same on all ships.. (they've been similar on the three we've been on) and the doors are HEAVY. My older daughter was 8 when we were on the Spirit in February.. and she STILL had a hard time pushing the balcony door open.. My 3 year old couldn't open it at all... and would just come stand by the window and knock til we let her out with us..
I don't think you need to worry about your child "escaping" when your back is turned..
Carnival Miracle to Aruba/Curacao/Dom.Rep/Grand Turk - 3/11
Carnival Miracle to Panama/Belize/Costa Rica-1/10
Carnival Sensation to Bahamas - 8/08
Carnival Spirit to Acapulco/Zijuantenejo/Manzanillo- 2/08
Carnival Miracle to Bermuda/Newport,RI - 4/07
Carnival Legend to Jamaica/Grand Cayman- 4/04
Carnival Imagination to Barbados/Martinique/St.Maarten- 2/03
Carnival Victory to San Juan/St. Thomas/St.Croix- 2/01