Canning with Quart Jars
Increasing the size of the jar generally increases the canning time.  When processing, you are heating the food all the way through to a particular temperature to kill any microbial contaminants.  For an item with more volume, it will generally take longer to bring the center up to a particular temperature.

How long you have to process it depends on how big of step you take in the size of the jar, and what you are canning.  I would imagine it would usually add 5-10 minutes to the processing time.

Here is a link explaining it. It also refences the USDA canning guidelines. The second link includes canning times for many items; most increase with larger volumes, but not all.  These should get you started, and you can research further if you are canning something that isn't in these documents. I suppose there is a general processing time that is safe for any size, but it would probably affect the flavor and texture of the food to process it too much more than is necessary.

NOTE: While I may play fast and loose with some USDA guidelines, canning is ALWAYS serious business. Improperly canned foods can lead to botulism, which is hard or impossible to detect, and you can't "cook it" out of the food.  Use tested formulas and correct procedures.

PS: Here is the direct link to the pickle guidelines. It looks like for anything larger than gherkins or sliced (bread and butter) pickles, you will add five minutes to the time. MAke sure though...