When I run My Butt feels heavy, is that Normal?

So lately I've started to try to run.

First, I'm trying to stop smoking, FYI doing well with that. I thought it would make running harder. My breathing isn't the issue.

 I ran track in High school for one year I wasn't good. I was very slow.

Anyway, I am enjoying it. But I can't run very long without having to stop. not because of my breathing but because my legs feel heavy and my butt feels like it's flopping around.

I'm not extremely overweight by any means. I'm 5'4" and 140.

Why am i tiring out to fast?

Because you're out of shape.  Keep at it and build up your time/distance slowly.   Give it some time and you'll be fine.

Is it okay that I'm Jogging at a pace of 5.3 for 4 min then walking for 5minutes.  What should my progression be?

There is the "Couch to 5K" program on line (aka C25K). It will help you get started.

If you just stopped smoking (YAY for you!!), go slowly with even the C25K. even 4 minutes of sustained jogging sounds like a lot for a beginner. Maybe that is why you are having trouble?

What is "ok" is what feels ok and sustainable to you. Only run every other day, especially at first. Walk on the days you don't run, but don't try to walk too fast. Be sure to start stretching as part of your jogging routine.

No one is keeping track of your progress, so never feel that you need to improve faster. As long as you aren't losing ground, you are doing things right. If you start losing ground (can't do one day what you did last time out, for example) you should ask for help.