I can't help but think of the sleepless nights, messes and all of the stress that babies cause! There seems to be a lot of stress in your relationship already and to add marriage and babies is akin to "asking for it", that is a really big blowup.
After 6.5 years I should think that most of the bumps would be smoothed out. Not gone, just not major events anymore. The fact that they are not is a signal that there is an underlying problem or problems that needs to be settled before going further.
You probably already know the solution to some parts of the "puzzle", so you need to set aside your fears and look at the situation in a rather detached way. Lists always help me! I would list the good things about us, the not-so-good things, the bad things and the things that definitely must change. [Remember that this is the way you see it, not the way some outside judge would.] By putting it down on paper in a four column balance sheet you get a look at what you have in a different way.
This is the method that a lot of counselors use because it has proven reliable, especially when each partner does it alone and then the results are put together. I hesitate to recommend do-it-yourself counseling, so it may not be a good idea to try it on him just yet.
Once you have a good look at your own list and clarify the problem points, it would be good to get counseling, but if not possible, start to work the list with him by introducing one thing at a time and trying to get an agreement on change. If you can get rid of all of the "definitely must change " items and make some progress on the "bad" items, then I would say that you have found the right partner.
You may find that the process is a bit discouraging at first, but remember that "the pigmys eat an elephant one bite at a time". Try to approach your problems in the same way and collapse one thing at a time. Your anxiety levels will go way down and your confidence will go way up! That's a double win!
Finally, I will throw in a moral note that you may accept or not. For centuries, we have known and seen that relationships work best based on honesty and love. The Golden Rule: Do unto others as you would have them do unto you. It is absolutely critical in marriage. Nothing is as destructive as lies. Nothing is as powerful as genuine love.
God bless you and guide you on your quest for a loving relationship.