Some beers are classed as "doublebock" and some as "triple bock". Doubles seem to be a little stronger (higher APV) than average and triples seem to be stronger than that, but is that they definition or an effect? What exactly is being doubled or tripled in the production of these beers, and is the primary goal strength or some aspect of flavor or something else?
Doppelbock (or double bock) is intense in its maltiness and higher than "single" bock in terms of alcohol content, typically starting around 6-7% and going up to around 13%. There isn't anything specifically doubled or tripled; rather, doppel idiomatically refers to be being "bigger"/stronger than a standard bock. In terms of how higher "maltiness" is accomplished, that would depend on the specific beer; mashing at high temperatures, reducing lautering, using certain grains or different yeasts, and other factors all can increase the maltiness of the final product.
A triple bock would just be a naming convention emphasizing even further the maltiness and alcoholic strength of the brew.
As an aside, doppelbocks are an evolution of strong monastic brews used as "liquid bread" for fasting monks, as they were not allowed to consume solid food. These sweet, malty beers evolved over time into the modern doppelbock.
Typically, it seems people expect single, double and triple to mean higher alcohol content. But that is not exactly true.
You have single and double bocks with the same alcohol content. Take Weihensthephaner for example (a respected 1000-year old monastic brewery): Weihenstephaner Korbinian is a double with 7.4% ABV. Weihenstephaner Vitus is a single bock with a higher ABV of 7.7%. In this case, the single has a higher ABV than the double.
More grains and more sugar do not equal more alcohol. The strain of yeast and temperature determine the survivability. Some yeast can live at high alcohol levels. You can feed them all the sugar and grains and they will still die and stop fermentation (producing alcohol) when the alcohol level 'limit' is reached.
The eisbock gets a higher ABV by freezing the beer and removing ice. This removal of water is how the alcohol content is increased. Again, most yeast cannot reach 12% (which one typically finds in an eisbock).
The single, double, triple label has to do with the strength of the beer overall, including nutrition (calories) and taste. Remember, these 'doppels' were created for sustenance.
Careful with the word 'stronger' when talking about bocks. It can mean more malty, darker, fuller, not just higher alcohol level.