OK, can't get this out of my head, so posting a second idea.
The answer to the riddle is:
a lottery or raffle ticket
This thing can be so tiny,
That's when it has the most variety.
Lotteries with lots of small winnings can have more variety.
Standing up straight, it is surrounded,
Otherwise it can make things bounded.
When still in the convenience store, a dangling string of lottery tickets is surrounded by other tickets. Otherwise the tickets are still wrapped around the roll, i.e. bounding it.
Within a box it lets you choose,
But if it points up you will lose.
Sometimes you have the tickets in a box and somebody picks one. Not sure about the pointing up, but losing definitely is something that goes with lotteries!
It can be seen leaning,
That's when it reveals true meaning.
Some tickets have a lenticular or hologram that make you look at an angle to see what you've got.
It can be a celebrity and nothing at once,
It can show uncertainty but never incoherence.
This part fits well -- a lottery ticket may be highly valued by its owner ("celebrity") even though it is not going to win and is therefore worthless. It may be as of yet "uncertain" whether I'm going to win, but it will never be "incoherent" - there will always be a way to definitively tell whether you won or not.
But when wealth is what it shows,
The end, you will know.
At some point every ticket either shows wealth, or lack thereof. Either way, it's the end of this ticket.
By the way, I despise lotteries and do not participate in them, this was just an idea that came to mind. :)