16-month old cries every night - why?

Can anyone help me figure out this mystery?  My 16-month old wakes up
between midnight and 2 am every single night and cries very loudly. He
just wakes up every night without fail, sits up and cries, with his
eyes closed.  He says "No, no!" and pushes us away if we try to pick
him up.  Generally a bottle will console him, but at times times he is
too upset even for that. The past couple of nights, he accepted to be
carried in our arms and then went to sleep again with a bottle.

We have not been able to change the pattern whether we feed him a lot
or a little for dinner, or whether he has had a particularly busy day
or not.

It's so bad that our condo neighbours have complained, which prompted
us to look for a single family home.  We're moving this week in fact!
Still, we would like to figure out why our little one cries.  It's
been going on for months and months.  I don't remember the last time
he slept through the night without crying at least once.  Some nights
he wakes up multiple times too.