I just want to jump in and say that it is really awesome of you to be able to recognize and put all feelings aside and help your DD.. My cousin is morbidly obese (she wears a size 16 women's at the age of 12) and her mum is completely in denial about it all! So I really want to give you massive kudos for taking that first step!

Also, sometimes weight issues can be genetic rather than learned.. Perhaps take her to the doc and have a full check up done and provided everything is ok then get her into some sports! There is so many different sports around, swimming, tennis, netball, soccer absolutely anything and let her try it all and see what she enjoys, sports are fantastic for kids and they play on weekends and usually there is a training session during the week! We are still experimenting with our DD (also 6) to see what sport she really takes to. We have found that swimming is always a winner! If you have a local leisure or swimming centre then sign her up to some classes of an afternoon, they get a really good work out and they have a blast as well (not to mention bed time is a whole lot easier)..
With regard to food, don't deprive her of 'kid food' but she should also understand what is good food and what is bad food.. Although this will not stop her wanting the junk food!!
A few tips that I can give and also what I have found works is making sure they have a good breakfast (porridge is a really good one because it keeps them full, just add a bit of honey for some sweetness and they love it), pack a good lunch for school (sandwich, fruit, vegesticks, Little cheeses, they have some really cool stuff if you look in the health food aisle rather than the junk food aisle) and afternoon snack has to be something that is prepared not just grabbed out of the cupboard - I find when my DD gets home from school she is always hungry and wants to rummage through the cupboard but I won't let her, she can have another sandwich or I will make her some poached eggs with toast so she can dip them, something filling that will tide her over until dinner and stop her snacking all the time (because kids LOVE to snack!!) they are like little puppies that will just eat and eat and eat until they explode!

I'm assuming your DD is now in school? This is another good thing because they will be running around at recess and lunch as well

Even though my DD is tall and slim I'm still conscious of teaching her healthy eating habits, but as I said I want her to be able to enjoy eating kid food. I think kids who are deprived of being able to eat junk every now and then (whether is some ice cream or a bit of soft drink or even a cheeky happy meal) tend to "pig out" when the opportunity presents itself!
I can always pick the kids who get fed carrot sticks because they are the first to the lolly table at every party, whereas my daughter sees it as no big deal!