Actually, you aren't overloading the genny, you are drawing from the battery. I'd be caught trying the lights with the genny first, then if you find the battery going down too fast, either add a second battery or go ahead with the alternator.
Thing is, an alternator, say a 65 amp unit, will not put out anywhere near its 65 amps unless it is (A) warm, and (B) almost at max RPMs. If you are rolling your diesel at 1800 RPMs, your 65 amp alternator may be pushing out, oh maybe 20 or 30 amps on a good day. Changing the pulley ratio will help.
Now your genny is making 14amps no matter what. Spin it, out comes 14 amps (goes by winding size, etc.). This is why they put one on there in the first place.
Again, a second battery may do a better job of running your lamps. Tally up the total watts, divide by 12 and that will give you the total amp draw. Multiply that by the number of hours you run the lights per day. Now you know the total amp-hours you need to have in your battery.
For example: 2 55 watt halogen work lights, plus 2 55 watt headlights plus 4 10 watt marker lights equals 260 watts divided by 12 equals 22 amps times 4 hours, so you need a battery with 88 amp hours storage. Lets round that up to 90. If your genny is charging at 14 amps, you are really only taking out a mere 32 amp hours total. Well within the capability of your battery.
If you double the size of your battery by adding a second one, then you will discharge both by half. It is well proven that doubling battery capacity more than doubles the battery life.
