We have a balcony outside our bedroom that has a far drop below. I would NEVER trust my boys not to jump through that railing if they saw a rabbit or squirrel. They jump first and think later.
What we did was buy clear plexiglass from Home Depot, and nailed it to the railing. It looks good and the boys can look through it. And I am not a nervous wreck!
In the meantime, I would put up cardboard or something that would prevent him from looking over.