US baking recipes are generally based on (US) large eggs. (I'm not sure about other countries.) Some recipes even explicitly say that. If you've been using (US) jumbo eggs, then you're using ~25% too much egg in your baking. The effects of that will of course vary from recipe to recipe. It's not so much that large is "optimal", but rather that it's what the recipes are calibrated to.
You'll see several standardized sizes of eggs in the store:
- Jumbo: > 2.5 oz. (71 g)
- Very Large or Extra-Large (XL) > 2.25 oz. (64 g); 56 mL (4 tbsp)
- Large (L): > 2 oz. (57 g); 46 mL (3.25 tbsp)
- Medium (M): > 1.75 oz. (50 g); 43 mL (3 tbsp)
I got this from wikipedia's article on chicken egg sizes, which also lists egg sizes in other countries, which others in other countries could compare to the US sizes!
Long story short: It's the acid, and any acid will do.
Food colourings are a type of dye known as an acid dye. Their effectiveness relies on hydrogen bonding which only works in an acidic environment.
It's not that the vinegar does anything special - not exactly. Rather, adding a few drops of food colouring to a large amount of water would give you something that's not acidic at all, which will diminish or totally eliminate its effectiveness as a dye. Including vinegar in the mix simply allows you to stretch your rations, so to speak - to dilute the colouring in a whole lot of liquid without making it useless as a dye in the process.
Basically, you're creating a dyebath, which is a well-known term in the textile world, as it's used to dye wool and other fabrics. Warm temperatures (140-180° F) also aid in dye absorption, and apparently - although I'm no expert in textiles - a small amount of Urea also helps.
You could definitely use cream of tartar, citric acid or any other acid, but the recipes using vinegar are generally aiming for a specific pH, so you'll want to adjust quantities of any other acidifier to match. Presumably, vinegar is just the cheapest and most widely available acidifier.
Best Answer
The proteins in a fresh egg are too viscous, even when thoroughly beaten, to wash a baked good.
The water thins the proteins so you get a nice glaze instead of a layer of scrambled egg.
Older eggs have sometimes degraded enough that they don't need the water but it is easier to always add water than to make a subjective judgement on the state of your egg proteins.