Does volume of risen starter effect rise of dough

It sounds like a vibrant and healthy starter - use it.

The problem is that no starter can guarantee the shape of any loaf because a lot of things factor into the puffiness of your loaf. Did the kitchen heat/humidity create a lot of gas? Did you fold the dough enough times and rest it long enough between the folds to create a enough gluten? 

And then there's the oven environment. It needs to heat up right to get the loaf to release steam and spring up. 

You could have the most powerful starter in the world, and your bread may come out "flat-ish." And then, next week, when your starter barely doubles, you might end up with something that looks like a hot air balloon.  

You can't let worry over the starter keep you from trying and seeing what you get. Focus, instead, on what you can control, which is making sure there is plenty of gluten. Give the dough some kneading/folding after autolyse when you mix in the salt. Give it a little extra time between some of those folds, more like 45 minutes rather than 30. If it gets pillowy and you see gas bubbles under the skin, then you're on your way to having a good loaf of yummy bread no matter whether it ends up looking like the Taj Mahal (high and round) or like Hagia Sophia (a gentle dome). And when it comes to shaping, do so gently, so as not to de-gas it, but so that it's tight and high. That final shape can really help with getting the results you're after. 

Liz, A few years back I asked that identical question. Like you, I wanted my starter to be the very best it could be. Although it is true, that an active starter is necessary to get 3-4x rises, there another huge factor.

For a starter to rise super high, the gluten must be well developed and strong. Without a good gluten network the starter will not be able to contain the vast amounts of gas necessary to push the surface of the starter upwards.

Think about this. Consider the difference in a dough using white flour with 65% hydration an another with 100% hydration. Think about how much gas each dough would hold. It’s much the same with starters.

If you want to see how high your starter can rise, mix your starter at 65% hydration and make sure it is kneaded well. Keep the in mind that a drier starter will take more time to rise than a wet one.

Dan