That's freaking looking! What kind of tomato is it?

Park's whopper

It is happening on every branch on the upper half of my 5' tall plant

Looks like something happened to that plant about 6 weeks or so ago that caused fusing of some stems in what was then a new developing growth tip.

FAIK there is no real official explanation for it, just speculation that it is some sort of genetic response to a shock of some kind.

Somewhat like what causes the megablooms and fused stems one sometimes sees when the plant is suddenly exposed to a spray of some kind, a pest attack, or an unusual cool period when newly forming. Sometimes the fusing is terminal for the branch or tip but sometimes the plant overcomes it and tries to recover. When it does the new growth is always weirdly deformed.

I have noticed with the newer version of Park's Whopper called Park's Whopper Improved that it is prone to more fusing with new growth. I have 4 of them growing and all have fused stems that I attribute to the weird weather patterns this past spring right after plant out.

I'm not saying that is for sure what this is, just reporting on the speculation based on my reading and personal observation. I'd be inclined to let it grow and see what happens just out of curiosity but you can always trim it off and let normal growth replace it.

Dave