You're spiritually "grown up" or mature when, through practice, you have trained your senses to discern between good and evil. You've practiced walking in the spirit and renewing your mind by the Word of God until even your flesh habitually goes God's way instead of the world's way.
Stop and think for a moment. Aren't there some things your old flesh used to pressure you to do before you made Jesus Lord of your life that you don't even want to do anymore?
There are for me. For example, I used to smoke tobacco, and I felt sorry for all those Christians who couldn't. But you know what? Now that I'm a believer, I have no desire for tobacco anymore. It is not even part of my thoughts, much less my lifestyle.
That's the kind of thing that happens as you feed and renew your mind on the Word of God. It doesn't necessarily happen quickly or easily. Your flesh may fight and buck for a while because it's been trained to go the way of the world so long. But if you stick with the Word and keep growing, your flesh can develop the habit of righteousness just like it developed the habit of unrighteousness.
Don't starve your spirit by trying to get by on just a little spiritual milk now and then. Develop the habit of feeding on the solid food of the Word every day and find out what real maturity is all about.