Uh-oh, two "Toms" here now!
Tom-TVE..., I'd still take a peek under the plastic and see if there is anything living there, i.e., ants, wasps, etc. Ya never know. I also wonder if that plant is a different variety than the others; perhaps it is more susceptible to excessive heat or something. (Again, just wondering out loud.)
Asl for "blight", that has become an umbrella name for the many different kinds of "blight". But again, no blight of any kind is involved in that weak-looking plant so you sure are doing well there. And yes, solarization (putting down your tarp) sure helps to inhibit diseases (and certain weeds). Congrats to you on a great garden!
Maine-Tom, BER often goes away as the plant progresses. Many times the early fruit will suffer from it but the following fruit will be just fine. Lime tends to take a while to kick in and is not a quick-acting fix so that might not have done the job for you. It also will change your pH, which will certainly help with calcium uptake or, if you've changed it too much will inhibit it. If you are growing in containers and using "store-bought" soil then by all means add lime to your soil mix.
Looking forward to ya'lls pics of your next tomato sandwich!
Shoe