How to handle my cute, playful but mean boyfriend?

I am an over sensitive girl and easy to become moody. At first, I met my boyfriend, he is a happy and playful guy who always being funny and teasing in a cute way. He often ask me why so serious and told me the need to be fun and playful to get rid of stress and negative feelings. I agreed and his presence making me getting better and positive. But months later, he begin to become more possesive and on date, he wouldn't want me to leave his side even just for minutes whenever we go. Maybe he wants people to recognize that I am his. He said that I am too attractive that he wouldn't like it if anyone see me in less clothes. He begin to show his rough side - he put his arms around my shoulders and holding my arms a little rough sometimes, he tease me in mean way and think its funny. He would stop when I begin to sulk or to cry. And then he slowing down his behaviour and apologize. He said he was actually a rough guy and could get carried away. But he still trying to treat me warm and soft as far as he could when I need his support or advices. When I begin to act tough or fight a bit, he says he need my soft side that I show him all this time which making him happy. Is this healthy?
How to handle my cute, playful but mean boyfriend?
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