Since you can see this when you equip the gear, I did a little test with no master gear on except for +1 level automaton gear. At ML40, with the Spiritreaver M-400 head (ie blm head) and Stormwaker Y-700 frame:
My auto's default HP was 1892, MP 1815, and base stats were all +0.
Melee - 423, Ranged 10, Magic 474.
Upon equipping a Kara earring +1 (so automaton level +1):
HP was 1892, MP 2032, and base stats were all +28.
Combat stats didn't change. So, I gained 0hp, 217mp, and 28 base stats across the board.
Upon equipping the Mpaca's boots (so +2 automaton level total):
HP was 1898, MP 2036, and base stats were all +30. My auto gained 6hp, 4mp, and 2 additional base stats.
Upon equipping the Visucius's Mantle (ambu cape +3 automaton level total):
HP was 1904, MP 2042, and base stats were all +33. My auto gained 6 more hp, 6 mp, and 3 additional base stats.
This doesn't include stat additions from gear, or exponential increases from maneuvers, etc. I don't have Varga Purnikawa, so can't say if the +3 automaton level stat gain trend continues above +3. But, in theory, +3 more would give 6-9 more base stats to the automaton in addition to hp and mp.
How does that translate to damage? Well, every weaponskill formula is based on stats so an increase in a specific WS or magic stat would also increase the damage. I'm not good at math so I'll let someone else figure that out.