It's faith, not tears, that proves the reality of repentance. David, a man after God's own heart, did sometimes weep over his sin, but not always. In that notorious instance when he sinned with Bath-Sheba, he tried for nearly a year to cover his sin without any evidence of remorse. What marked David as a man after God's own heart was his faith, not the quality or depth of emotion associated with his repentance; not even the speed of his repentance.
Few people are genuinely and perpetually sodden with the sorrow of remorse all the time. And that is a good thing. As Christians we are commanded to be joyful and always rejoicing. The very thing David prayed for at the end of that year-long rebellion was that God would restore to him the joy of his salvation. There is a legitimate joy in salvation that in the usual circumstances of life overwhelms and overshadows the sorrow of repentance. That joy is a better gauge of your spiritual health than the feelings you get when you ponder how sinful you are.
As believers, we confess that in and of ourselves we are utterly wretched, so it is fitting that we should have sorrow (James 4:9). In fact, we will never be completely finished grieving over our sin and its destructive consequences until God Himself wipes away our tears in heaven. There certainly is "a time to weep . . . a time to mourn" (Ecclesiastes 3:4).
But that same text says there is "a time to laugh" and "a time to dance" as well. We don't have to wallow perpetually in the shame of self-reproach in order to prove our repentance is real. "Blessed are those who mourn, for they shall be comforted" (Matthew 5:4). After all, God's "anger is but for a moment, and his favor is for a lifetime. Weeping may tarry for the night, but joy comes with the morning" (Psalm 30:5).
If you hate sin and love Christ and confess before Him that you are indeed a helpless sinner, then I wouldn't be over-analytical about the emotions you feel when you confess your sins. That kind of introspection will make you a fruitless Christian. Did you ever notice that qualities like regret and misery are missing from the characteristics of the fruit of the Spirit? (Gal 5:22-23)
Scripture says, "Examine yourself to see whether you are in the faith"—not, "Dissect how you express your repentance to see if you have been piteous enough."
My advice to you is to cultivate faith, not an emotional response. Emotions by definition rise and fall. They are neither the instrumental cause nor the evidence, much less the ground, of our justification. Faith is the instrument of justification, and the work of Christ is the ground of it. Focus on that, and your faith will grow, your joy will increase, and your emotions will take care of themselves.