I am not expert in teasing. I do not use it much as I find it to be a risky affair. If it goes well, she will love you, you go too far and she will hate you. It is difficult to figure out the fine-line between the type of teasing that is sexy and which is not. Generally speaking the more compliant she is from the get-go, the more you can get away with. Teasing is a bit like escalation in that regard. The more she likes you, the more bold you can be. The lesser the compliance the more careful you have to be. Go too far too quickly and it may hit her the wrong way.
Additionally, just like escalation, you have to go out and try it, fail and succeed in order to find the sweet spot. since all women are different and so are EVERY encounter, you will have to develop a gut-feeling on the spot on how far you can go, by creating an awareness and understanding of the situation. This is only done through field experience.
Now that said, you can use assumptions to tease someone if that is your thing. Again it is not my thing. If you want more expert detail on teasing, you may want to ask this question to someone who uses teasing as an active component in their game.
Beside what I have written about calibration (which again in only acquired through field experience), certain rules regarding social common sense applies. Teasing based on a negative stereotype goes against such notion and should be avoided in most situations. She got upset and I totally see why. Girls and people in general who are from ethnicities or cultures that are prone to stereotypical judgement tend to be rather sensitive when it comes down to being "teased" about it. I would not even call it teasing, I would call it rudeness.
I personally prefer "fun" and "silly" comments that are fun, that does not make the girl look or feel bad. You example with the cheese thing followed with "you suck" is overly negative. Additionally, you seem obsessive and weird. Who cares about how she eats and what eats? you only come off as obsessive and compulsive.
Instead tease her on something funny that few people would react negatively too such as:
"You seem like this very conservative gir who goes to Sunday school" (exaggeration is good)
"You remind me of Sara (implied social proof), Sara was secretly a serial killer. are you a serial killer - please don't kill me"
"You seem like such a feminine woman who was nuts about pink when you were kid"
There you go. No harm taking, no offensive statement, no passive aggressiveness. All good vibes. People love and chase good vibes. Be the provider of excitement, fun and overall good vibes.
And... this has nothing to do with group situations, although that could amplify the issues you created.