How to have different dynamics in each hand on piano?

At this time, no. (I think I've heard about it being on the list to be put back into version 4.x eventually, but I'm not sure of that and don't know when it might be if that is actually the case.)

However, you can fiddle it. Add two pianos to the score. Remove the bass clef staff from the first and the treble cleff staff from the second. Add the appropriate bracket. Copy the notes from the original piano to the new double piano. Since the bass and treble clefs are not the "same instrument" they can have different dynamics.

You can control the dynamics of single notes or selection of notes in the Inspector. You can select all notes in the left hand, for instance, and put an offset of -20 or -40 in the velocity box.

You wrote:
...the left hand and right hand are always equally weighted however I cannot figure out how to change this as sometimes the melody is over-ridden.

For score playback, you can select those "over-ridden melody notes" and change their velocity in the Properties panel's Playback tab.
Here's an example where the last 5 measures have the velocity of the melody (treble clef) increased from 64 to 80:
change_velocity.mscz
All other notes remain at 64:

You also wrote:
Is it possible to have different dynamics on each hand?

For writing two different dynamics (one per clef/staff) in the score, you can use a "real" dynamic from the Dynamics palette on one staff along with a "fake" dynamic (on the other staff) taken from the 'Symbols' section of the Master palette.

--OR--

As suggested earlier, use 2 pianos - with each piano playing a different clef/staff.