If you are looking for a 300+ yd. deer rifle, then cartridge selection is going to be important. You will need something with a lot of downrange energy. I would suggest either 7mm mag or 300 WM. With either cartridge, a very light rifle would not be that advantageous. Third request was that it was left handed.
I believe you would be best served by the Ruger [email protected]
Left Hand. It is available in both 7mm mag and 300WM. Strange as it may seem, their specs state that the 7mm is a bit heavier at 8.25lbs vs. the 300 at 8.00 lb. Both have 24" barrels.
I hunt almost everything with a Ruger M77R in 300WM. It has harvested a lot of deer, elk, even a couple of bears and 2 Moose. It has been my companion in the field for over 40 years and has never failed me and at my age, I am certain it will out last me.