Is it normal to hate when my little brother does this?

Normal for both of you. He'll quit asking soon enough and go his own way. Maybe you could do some family stuff with him though. It sounds like he's missing a friend

A better way to explain it might be that you are doing more adult stuff that is not appropriate for him yet.

And, then schedule with him some stuff that you do together that is age appropriate for him.

My Grandfather smoked his whole life. I was about 10 years old when my mother said to him, 'If you ever want to see your grandchildren graduate, you have to stop immediately.'. Tears welled up in his eyes when he realized what exactly was at stake. He gave it up immediately. 

Three years later he died of lung cancer. It was really sad and destroyed me. My mother said to me- 'Don't ever smoke. Please don't put your family through what your Grandfather put us through." I agreed. 

At 28, I have never touched a cigarette. I must say, I feel a very slight sense of regret for never having done it, because your post gave me cancer anyway.

I mean you are being responsible but I think your sibling just wants to spend time with you. I think maybe explain you are doing adult stuff he isn't old enough for yet, and tell him you will do age appropriate things with him later. Maybe something he's really into. It doesn't sound like.he is trying to burden you but sounds like he likely follows as he cares about you and you saying no is in his mind telling him you don't want to spend time with him.

You're the big brother and it's normal that your little brother (who obviously loves you) wants to hang out with you.
No need to make such a fuss of it. You just calmly explain to him that he is too young to go to these places because people consume alcohol and it might be unhealthy for him.

Big age difference, I had the same issue but we were only a few years different in age and I was the young tag along.

We do not like it at the time, but we will eventually grow to understand. It's just part of growing up. Life is full of things they're going to have to be a certain age to qualify for. You are in the position of teacher and because you care you will handle it better than some stranger.

F--- him.

pretty fucking normal, pretty fucking annoying

Sounds like he just wants to get out of the house and do something with you. Enjoy it while you can, you may regret not doing so in the future.

It is normal

Its good that atleast when he cries you feel empathetic. My older sibling was cruel. I wouldnt even ask to go with them they'd probably cuss me out.