Being Scared of Heights? Is this an innate phobia?

Today, Big Brother, Baby Boy and I went to my gym to work out.  When we got there, I took them to the nursery.  This was their first time to go, and my gym is really open and has stairs to access the upstairs nursery.  When you get up the stairs, you can look beyond the rails and see the courts below you.  Anyway, Big Brother has always kind of shied away from stairs and is really timid and careful when on them…(that actually describes his personality to anything new).  We got up to the top (after being really careful and holding onto the rail and freaking out a little) and I thought we were doing good.  That is, until I got a little ahead of him and turned around and watched him to make sure he was following me.  I saw him looking out over the courts and his eyes just got wild.  Then, all of a sudden, he squatted down and looked scared and called for me.  I instantly went to him and told him it was okay.  He was about 10-12 feet from the railing where you could look down, so there was no worry (of mine) of him falling.  I put my arm around him and told him to hold on to me and walk and close his eyes.  So, we made it to the nursery with me leading him while he had his eyes shut. 

Now, I ask–is this an innate phobia?  My mom is scared of heights.  Could this be genetic?  I don’t really know much about it.  I am going to find out more (good old internet   ).  I have to say it doesn’t shock me that he reacted that way.  I feel bad for him since he is my baby, but I have to say I was looking forward to the roller coasters with the boys once they got older.  I guess that won’t be happening.