Tired is based on a lack of sleep. It can many times be fixed by a trip (or 3) to the local coffee shop. Latte, please :-)
But weary ... oh weary is a vicious animal. It is physical, emotional, and spiritual. It is fatigue deep into your innermost being. Weary begs you to give up. It tells you that you just can't go any further. 20 lattes won't fix weary.
There is only one answer for weary:
Matthew 11:28-30 "Come to me, all you who are weary and burdened, and I will give you rest. Take my yoke upon you and learn from me, for I am gentle and humble in heart, and you will find rest for your souls. For my yoke is easy and my burden is light."
A yoke is a beam that would be placed on the neck of two oxen, so that they could work together to carry a heavy load.
Jesus tells us to take His yoke upon us. Picture it if you will: Jesus walking right alongside you - linked to you - right in step with you - carrying the burden WITH you.
The burdens that we carry are just that - burdensome. But they are also precious cargo. We don't see them that way when we are going through it, but they are being used to mold and shape us for greatness which is a great gift (if we will accept it).
Seeing burdens in this light, helps me to keep a positive attitude. There is a helper, Who always has my very best interest at heart. There is peace in His presence, no matter what else is going on.