My girls are 6.5 and almost 4, and being that my older one is also very sensitive and dramatic, I know where you're coming from. I discovered that my older daughter is also very perceptive and can be incredibly manipulative! Many times she'll use tears and accusations of me not loving her as a way of getting what she wants.
What has worked for us is for me to comment regularly about things that ONLY my older daughter can do. For instance, I will say, "Wow, it is so great how you're reading books all by yourself now! Isn't it fun to be able to read whatever you want, whenever you want?" or "I noticed how beautiful and graceful you were in your ballet class today! You were the best one in your class at the barre!" or even just commenting that I love the outfit she picked out for herself. Anything that allows her to feel special for being the older one. (By the same token, I also do try and notice things that my little one does that are special.) And, when the two girls are playing together and getting along great, I will compliment them both on that. Now that I have really been trying to notice the many good things they do, there has been a decrease in negative-attention-getting behavior.
That being said, there are times when I do need to correct my older daughter, and she does tend to cry about it. I just tell her, "It's my job to make sure you grow up into the best person you can be. I will always love you, I just don't love that you took your sister's toys away and hid them from her." So she understands that it was her actions that I had the problem with, and that I'm correcting her out of love in order to make her a better person. (Although she will still cry and carry on - no getting around it, I'm afraid!)