You certainly arent' the only person who would pay 2x the price for something that small. They price the 1/4ct range the way they do as entry-level pricing, the stones that size are generally fairly inexpensive anyway, even for very high color and clarity combinations, simply based on size. They want to get someone in the door to pay for their first Tiffany item. They could charge far more for those smaller stones than they do. But they're banking on that item being what puts the wearer into the "my next item needs to be from tiffany's and nothing else will do." It's a marketing thing.
However when you start getting into above 1/3ct-1/2ct range and beyond, that's where the prices will start to steeply rise. You're getting into Engagement-Ring-size territory there, and while the average TPF e-ring size is much larger, the average e-ring size at least in the states is about 1/3ct. They're going to price those at a much higher profit ratio as that is their bread and butter. They are also starting to go up in price just based on size to spec ratios just in the open diamond market.
Your comment above about a larger stone with lower color and clarity vs a smaller stone with higher color and clarity is pretty standard even outside of Tiffany. The lower the color the bigger you can usually go in the same price range. Color in an ideal cut stone tends to dictate price more than clarity does in most cases in terms of pricing for size. So yes, you will maybe get a 3/4ct stone I VS2 maybe for the same price as a 1/3ct F VVS1 stone. That's maybe a bigger price jump though than you'd think, Tiffany or not. The way I always learned that is that color grades are roughly $1K more per higher color grade, and clarity is roughly $500 more her clarity grade higher. That's just basic and there's MUCH more factoring into that, and the range could be higher or lower.
Tiffany will mark up anything they sell more than an average brick and mortar or internet vendor as you are simply buying brand. They are in theory selling "peace of mind" because they have hammered home that Tiffany=Quality. Which I might add doesn't work for everyone.
For your daughter's first diamond ring, I would probably stay 1/2ct or smaller for the main stone.