Heirloom varieties don't have all the disease resistance bred into them that hybrids do.
The tomato plants pictured have some kind of fungal disease. Since the leaves are so far gone (and I'm no expert on diagnosing different diseases) I don't know if it is a blight or wilt or septoria, but they are all fungal diseases with basically the same treatment.
Remove all the infected leaves and then spray the whole plant, especially the underside of all the leaves and the soil around it, with some plant anti-fungal.
Plant anti-fungals include a milk solution (type it into the Search the Forum feature for instructions), baking powder solution,
1 tablespoon of baking soda
Ã‚Â½ teaspoon of liquid soap (not detergent)
1 gallon of water
hydrogen peroxide sprayed straight from the bottle
or organic commercial products such as Neem Oil and Serenade.
Pick one and try it, don't try mixing stuff, they can counteract each other. Re-apply or try a different one after a week or after it rains.