assume the 6oz acts half way along the arm, so the torque is 3.5in * 6oz = 21oz* in
47 oz*in - 21oz*in = 26oz*in
26 oz*in/7 in = ~ 4 oz
This is assuming worst case scenario, where the arm is perpendicular to gravity.
Cheap standard servos start at around $10 for ~50 oz*in. A decent servo is the Hitec HS-645mg, which has 100+ something oz*in torque, and metal gears, for around $30. Blue bird and Cirrus (identical) make a similar servo that costs around $20, but the quality isn't the same as the Hitec.
You can consider using levers/springs in order to help lift objects.
Check some of these videos out:
They might not be the best designs but theres much that can be learned...