We human feel that our dogs are caring towards us and they try
to make is feel better when we are emotionally upset. However, this is
the human side of the equation as we find it really comforting when
our pet comes to us in such situation.
The dog side of the equation is that this four-legged animal can too
feel the human emotion. However, different dogs will react to the
situation differently. Some may even turn worried, stressed, anxious
and upset.
Coming to what you asked, when your dog comes over and lies on top of
you, send him back to where he sits or sleeps. Take deep breaths and
try to be normal.