Answer:
I can run but not walk. Wherever I go, thought follows close behind.
It cannot be seen, it weighs nothing, but when put into a barrel, it makes it lighter.
What is it that has four legs, one head, and a foot?
Always old, sometimes new. Never sad, sometimes blue. Never empty, sometimes full. Never pushes, always pulls.
Slayer of regrets, old and new, sought by many, found by few.
I am the fountain from which no one can drink. For many I am considered a necessary link. Like gold to all I am sought for, but my continued death brings wealth for all to want more.