Jesus offers you a wonderful invitation when He says "come to Me."  He is the burden bearer.  He wants you to come and give Him your burdens because He cares for you.  He says, "Peace I leave with you, My peace give I unto you, not as the world gives, give I unto you.  Let not your heart be troubled , neither let it be afraid."  He offers you His peace.  He is in control and wants you to trust Him in your circumstances.  In turn for your trust He will give you rest for your soul, mind, will and emotions. 

The Apostle Paul puts it this way, "Be anxious  for nothing, (don't worry about anything) but in everything by prayer and supplication, with thanksgiving, let your requests be made known to God; and the peace of God, which surpasses all understanding, will guard your hearts and minds through Christ Jesus."  Philippians 4:6-7 (NIV)

When you come to the Lord with your burdens, He offers you peace that is beyond description.  This peace will guard your heart and mind because they are being kept in Christ Jesus.  Another way to think about this is to tell Him about your problems, your heavy-heartedness.  He already knows them but He wants you to give them to Him in prayer as an act of trust.  He will lift your load because He will be bearing it with you.

He loves you that much!  Satan will try to tell you this will not work.  Resist him and trust the Lord.  The Lord will not fail you.  He is faithful to keep His Word.  This is the "peace of God" that is being offered.

In a real encounter with worry, I took them to Him and He flooded me with peace.  It works!  Have faith in God!  My circumstances didn't change but I knew He was with me.  The Lord will never fail you!