Can each leg only supply 1/2 of the rated watts of the generator? Would a wattage meter for each leg be a wide investment when supplying generator power to a home in an attempt to manually balance the load?
The short answer to your question is yes. If you look at your generator, you will find that there are breakers for each of the circuits. For example, my generator has four breakers: one for each leg of the 240 receptacle and one for each of two 120 receptacles. The generator is a 5000 watt generator, which is just over 20 amps at 240 volts. Each of the two 240-volt breakers is 20 amps, which means that each leg of the 240-volt connection can provide 20 amps without popping the breaker. Each leg of the 240-volt service provides up to half of the generator's rated capacity, as you suggest.
This actually came into play when I was shopping for the generator. Before I bought this one, I bought a smaller one... perhaps 2000 or 3000 watts or something, which was just enough capacity to do what I wanted. Because each of the two 120-volt receptacles could only provide half the rated capacity, it wasn't enough to run the appliance(s) I wanted to run, because some of the appliances would exceed half the rated capacity and blow the breakers. This absolutely comes into play when sizing a generator, because (basically) all generators will be rated based on their 240-volt output, because that's what the alternator puts out. So if you need to run a 120-volt appliance that pulls 2000 watts, don't buy a 2500 watt generator. Each leg of the 120 service will only be able to provide 1250 watts. You need to size a single 120-volt leg of the generator to run your biggest 120-volt appliance, or whatever your biggest simultaneous load is going to be.
Additionally, you should consider the size of the breakers on the 120 receptacles if you plan to run a lot of 120 appliances directly off the generator. A good generator will have a big enough breaker to allow the full potential of the generator on each of the 120 legs, but that isn't always the case. For example, a 3000 watt generator works out to 12.5 amps. The 120 receptacles may only have 10 amp breakers, meaning that if you're pulling off the 120 receptacles, even if you perfectly balance the load, you'll only ever get 10 amps, or 2400 watts. The extra 600 watts that you paid for will only get used if you are running a 240 appliance. This can be circumvented by using a Y-cord that plugs into the 240 receptacle and manually splits out each leg of the service into separate 120 receptacles. Again: not all generators are designed this way. Quality ones will have the appropriate breaker size on the 120 receptacles. But do check! It doesn't matter what the rated capacity of the generator is if the breakers will prevent you from actually using it.
This whole paragraph is moot if you are pulling 240 off the generator and not running 120 appliances directly off the receptacles in the generator.
I'm not familiar with the practical effects of an unbalanced load on a generator, but I do know that you need to make sure that neither leg is overloaded with 120 appliances. Ideally, the load on the two legs would be more or less balanced. For 240 appliances, this is not an issue, since they use both legs of the 240 service simultaneously (that's a poor way of putting it, but it'll do for the time being).
