How do you deal with this?

when you figure that out- let me know- I have two teens who will both deny eating whatever it is that's gone missing...

stop buying the junk food!
I did that too - my son would eat a WHOLE bag of chips with salsa if we didn't put a nip on that one!
He goes thru the house like a junkie looking for crack when he wants something to eat! NO, forget about the healthy things like fruit!
But the worst is, he leaves it out instead of throwing the finished stuff in the trash!
UGGGG
so it' stays out till I see him the next time to tell him to throw it away!

The easiest solution to not have the sweet stuff in the house. If it's not there, she can't eat it.

I'm dealing with the same thing. Eating the junk and not the good stuff. I stopped buying the junk.

As for not throwing the containers away - I have no clue. Everyone in my house does it, including DH. All you can do on this one is say "look this is the shopping list, put what is done on it or I won't know to buy more."

Well, I've been tempted to put the dirty dishes, wrappers, banana peels & other crap that gets left laying around, on their bed, except, I'm afraid they would just dump it on the floor in their room, or worse, they wouldn't notice it there! Ugh- it's so frustrating. So when you find the magic wand that cures this slovenly behavior, please share! :0

I started to put things I wanted for myself in my room, my closet. If she is the only one who eats certain things. Stop buying it. Even if you buy ice crean for yourself but she ends up eating most of it. Stop buying it.  If you want ice cream. Just go out and buy a small portion. 

They do sell deap freezers with locks on them.

Is she overweight - even slightly? I ask this because I wonder if perhaps she doesn't want to ask, or throw away the containers, because she's embarrassed? If she's overweight, she could be embarrassed to admit she's eating so much, so she'll do whatever she can to try to hide it from you.

I would say, as others have, stop buying it. When I buy something that I really want for myself, I put it in my room where I am the only one who can get it. Everything else is fair game for the whole family, and I don't make them ask, per se. I tell my kids that if they finish something, write it on the grocery list so I can get more. And they know that if it's late morning, late afternoon, or close to bedtime, they need to ask - but that's only so they don't get a snack only to have dinner 10 minutes later. They also know that if they do stuff like you describe, the stuff goes away. They'd rather be open than lose it.

I am going to be devil's advocate because I have been through this (not sweets though)

I do not know your rules but I decided that you eat when you are hungry abd clean up after yourself. I set aside certain things that were off limits. My son would come home from school and eat a dozen eggs and then I did not have them for making dinner and things like this. I started finding the empty boxes in the trash of all places and my off limits stayed that way except occassionally.
Sometime I will tell you about a sleepover with a total of 5 teenage boys and gallons of icecream and other things lol.

If it is only sweets and she continues stop buying sweets for a while., everytime she does it.

Your child has to ask permission to eat?

Well perhaps my child does have better self-control but I buy food so it can be eaten. I do not buy any junk food. I worked in therapeutic care as an administrator and those kind of controlling behaviors around food usually lead to sneak eating and eating disorders.