Looks like age.

It might be early blight. The chances are good, with the right care, your plants will be fine. Remove a bunch of the lower leaves, so none touch the ground. Water carefully so that the remaining leaves don't get splashed. Mulching helps --- it prevents infected soil from splashing your plants when watering. Disinfect your clippers after clipping.

If it is blight, rotate your crops and pick a resistant variety next year. The thing about resistant varieties is they have to be resistant to the stuff in your area. "Disease resistant" can mean resistant to diseases not common in your area. For example, Bacterial Wilt is common in hot southern areas of the country --- not a problem I have in Maine. Cool night temperatures is conducive to late blight, a problem for me, but maybe not for people in Florida.

You without a doubt have Septoria Leaf Spot. It's often mistaken for early blight and vice versa, and I get one or the other or even both together every year. they are both soil borne fungi and common in most soils around the world.

Once infected with either there is no cure and once a fungi spore takes root in a leaf it will colonize the leaf and eventually fruit and blow out more spores attaching to more leaves in a continuous cycle. The cycle can only be stopped with fungicides with continuous spraying every 7 to 10 days and especially after a rain to keep it from spreading.

You will need a sprayer, a bottle of copper fungicide and a bottle of a Chlorothalonil fungicide and brands don't matter, read the labels completely and start spraying. The reason for the two fungicides is to alternate and start with the Chlorothalonil to get it under control then use the copper the next week and keep alternating until the season ends.

People also use an organic clay called kaolin clay they spray on the leaves which hardens and won't allow new spores to take root in the leaves. All these treatments will wash off with the rain so reapplication is required ASAP. The fungus spores need wet leaves to take root and usually when you'll see the spots appear right after a rain, or during a rain if it rains for a couple of days.

But before you spray cut off all the branches with infected leaves. You will not hurt the plant and the reason those bottom leaves become so easy for the fungi to colonize is because mobile nutrients have been pulled form them to be used in new growth above. The leaves are weak with very low resistance to fungus. You can take off all branches and leaves up to the first flower/tomato clusters, they aren't needed.

I have woven landscape fabric under my tomatoes covered with mulch along with irrigation tubing without a patch of exposed dirt with in 4 feet of the plants, and I still get septoria and early blight. I also move my tomatoes new spot at least 50 ft from the old spot every year and still get it, there is little you can do from getting it, only slowing the spreading with practices Sigrid stated above.