Yellow leaves can be the sign of many different problems including no problem at all as older leaves will often yellow and fall off.* Since you say that branches are dying back, I'm thinking it's the same ones that have yellow leaves.* Take a look at leaf and stem disorders here.
I'm thinking it's sunscald aka sunburn, especially if the spots are on the same side of the fruit towards the sun.*
...my green tomatos,I have patches,a little bigger than a quarter,that are a lighter color of green,almost white,and it is kind of sunk in slightly.It is only on the green ones.Is this some kind of sunburn or a blight?
Click on 'Leaf' and 'Stem' here.*
Please let me know what you discover.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.