Everything you've written screams to me that you have an eating problem, if not a disorder.
I'm a size ten, hourglass, but I'd like to lose some weight
Why is this? What on earth is wrong with being a size 10, hourglass shape?
My OH and friends laugh that my fridge is full of carrots (for the dogs) and condiments rather than proper food. When my OH comes over I have to pop to the shops to buy proper food (chicken, eggs, milk, etc)
Do you not think this is an indication that you're not feeding yourself properly?
I just graze on fruit all day though. So this could be the issue. I never said I don't eat (apart from those two one-week episodes). But I find it odd that fruit could have such an impact. On a daily basis for example I can have a punnet or two of plums, four apples, two punnets of grapes, some berries and maybe a banana. That's on top of my massive salad. I do have the oil in the tinned tuna. And the balsamic vinegar has sugar, right?
All of this is a massive amount of sugar. Yes, you'll be getting the fibre from the fruit, but apart from that it's all carbs. And balsamic vinegar is also hugely sugary.
I don't drink fruit juice BUT I drink up to two litres of caffeine-free Diet coke a day
I'm glad you don't drink fruit juice on top of all that fruit! But 2 litres of Diet Coke?!. This is so, so bad for you. It's not the caffeine as such, although that can't be great, it's the artificial sweeteners, as PP have said. It can provoke an insulin response by the body as if you were drinking sugar. Why on earth have you got to drinking this amount of artificial chemical stuff?!
Fruit-wise I mostly eat pink ladies apples and grapes. Lateley I've been snaking on microwaved corn on the cob. A couple of cobs a week. No salt, no butter
You'd be better off eating the salt and the fat! Again, sweet corn is hugely carby - the clue is in the name 'sweet' corn. As a snack, along with all the other fruit (sugar/carbs) you've been eating, this is way too much.
Having pointed all that out, as things that will be impeding any kind of weight loss, I still think that you have an issue with food which you need to deal with before you consider weight loss.