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A weak battery won't put more load on the charging system, but it won't be able to help the system as much during high consumption/low charge moments like at idle with the lights & other stuff on. If the battery has gone bad in a way that it won't reach proper voltage, like a shorted cell, it can load the charging system. The stator in a bike's charging sys. operates very differently than the alternator in a car and generally speaking it can't be damaged by overloading.
In the scenario with the truck eating alternators the likely culprit was the mixing of good/bad batteries more than the two bad batteries directly. Any time a battery bank has a mismatch of batteries the bank does funky stuff and all it takes is one bad cell within the group. I see this most often on boats since most cars don't use a bank of batteries. The batteries with least resistance to charging will get a good charge and the others won't killing them exponentially faster.
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