Can you post a pic - there may be a packing nut you can tighten, to add more pressure (like a hex-nut around where the stem comes out)...
I've never had a packing nut control how much pressure is applied to the valve seat and washer. Every valve I've disassembled has had the valve stem screwed into the bonnet that is screwed onto the valve body. The pressure exerted at the seat is determined by the threads on the stem screwed into bonnet.
Tightening the packing nut squeezes the packing material against the stem. This would help correct a leaking valve stem should the packing nut be lose or the packing material no longer created a tight seal. It wouldn't alter the flow of water through the valve.
I agree with Mattmag above. Just plan on replacing the valve. Gate valves should be outlawed for any residential application that is not cycled frequently and does not need to control the volume of water flow other than on/off.