Auto-spacing text boxes

I would add an expression to the rectangle size and position property of a shape layer below the text layer. You use sourceRectAtTime() to look at the text layer above the shape layer using ref = thisComp.layer(index - 1). First, you want to calculate the size of the rectangle and maybe add a little padding;

// Rectangle 1/Size
ref = thisComp.layer(index - 1);
b = ref.sourceRectAtTime();
xPad = 40;
yPad = 30;
w = b.width;
h = b.height;
[w + xPad, h + yPad]

Next, you work on the shape layer's position property and add in b.top and b.left;

// Shape Layer position;
ref = thisComp.layer(index - 1);
rPos = ref.position;
b = ref.sourceRectAtTime();
w = b.width/2;
h = b.height/2;
t = b.top;
l = b.left;
x = w + l;
y = h + t;
[x, y] + rPos

Next, you duplicate the shape and text layers and move them to the top (Ctrl/Cmnd + d followed by Ctrl/Cmnd + [

You should now have. a text layer, a shape layer, another text layer, and another shape layer. The next thing you have to do is offset each text layer by the height of the next text layer. You can do this by using refT = thisComp.layer(index + 2); on the Position property of the succeeding text layers. You will have to find the in-point of each succeeding text layer by using sourceRectAtTime(inPoint) and an if/else statement to start moving each succeeding text layer up when the new pair of text and background layers start in the composition. Adding an ease(t, tMin, tMax, value1, value2) to the mix will move up each new text/shape layer pair up as each new pair is added to the composition.

I don't have time to write out that expression for you. It's going to be the hardest one to set up. When the text layer/position expression is worked out, every time a new pair is added to the comp, the pair of text/background layers above it will move up in the frame. 

I hope this gets you started.