Before you use newspapers to kill off weeds, find out what kind of ink is used. Being in the publishing industry, I know that certain inks have additives that most people in Cure Zone would avoid like the plague. Our business has switched to a soy-based ink, but there may still be many newspapers out there that use older type oil-based ink. The soy-based inks would be fine to use, but think twice if it's oil-based. There are also more allergies associated with the older type inks. But, if you have a soy allergy, you'd want to avoid the soy-based inks, too.
If you plan on doing this, I'd suggest you call up the newspaper office and ask what type of ink they are using. THEN you can make an informed decision on whether you think the newspapers would be safe to use when preparing your garden. (Or even using with your pets ... when I was a kid, mom used to line the bottom of the cat box with newspapers before putting in the litter, and I know lots of folks use newspapers for puppies, pet rodents, etc.)