In my opinion, large zucchini are worth nothing except to feed to the pigs or chickens or toss in the compost. Small ones are delicious. Pick your squash when its at the height of flavor.

I tried to find a scientific answer but except for big zukes are more watery and have less flavor, I couldn't find the answer I was looking for. So, I'm just guessing that big zucchinis are going to make the plant slow down production. A plant's job is to reproduce and when zukes get that big, the plant knows its job is done.

"What I am curious about... if I let those squash get so big, do they also in some way lose nutrient density as they get bigger? Or is this like a sprouts kind of thing where the smaller ones are actually more nutrient dense, and letting them get bigger just adds more volume to, but the same nutrients?"

Since you aren't concerned with flavor, only the nutrient levels, then yes, due to all the extra water the large ones contain the less the nutrient density is. The nutrients are diluted too and you would have to consume more of the fruit to get the same level of nutrients.

The only use for the big ones like that is if you want to make stuffed zucchini boats IMO.

Dave

The bigger ones are good when either stuffed or shredded for quick breads. If you want to freeze some shredded for later use then you want the bigger ones. I always let at least one get big for this purpose. Otherwise, the little ones are best.

I like the big ones cut into finger sized strips for dipping. I disagree that the taste really diminishes. Small zukes don't really have much flavor either. And it doesn't make sense that nutrients quit coming into the squash as it grows larger. If water is coming in, it's dragging nutrients with it. Otherwise, at what point does it stop taking them in? And why does it stop? Makes no sense that there are fewer, just diluted. Seeds develop and a pithy cavity forms, but the meat around the cavity is still very usable. And the zuke skin is still very edible at larger sizes, whereas larger yellow straight neck squash develop a thicker warty skin, almost like winter squash or pumpkins might, that's nearly inedible. If you have younger smaller ones, eat them instead of the larger ones. But don't just wholesale discard the larger ones just because they're larger. I have some white patty pans that are as big as dinner plates that I'm purposely letting go just to see how big they'll get before they deteriorate. My garden is shot this summer now due to drought, so I'm experimenting. :-)

Would something like this low-cost refractometer help to understand anything better on nutrients?

http://www.coleparmer.com/Product/Low_cost_Brix_refractometer_with_ATC_0to_32_Brix/EW-81150-08 

I've heard of Brix used for sweetness - not sure how it applies to nutrients. But it might be a start, and within my low budget for such things.

I just find the seeds get annoyingly fibrous as they get bigger. Also they can develop a bitterness that children seem to be sensitive to.

Stuff em, grate for bread or to add to soups/stews, food processor and freeze for soup base or add wheels and race them! I actually got a request from freecycle a few years ago for large squash for races at a family reunion! I gave them several mystery white squash that had got out of hand (huge) NT