When the flesh does not mean the body

"The spirit indeed is willing, but the flesh is weak."  --Matthew 26:41

In the UM doctrinal standard Notes on the NT, Wesley equated the spirit with "ye yourselves" and the flesh with "your nature."  Maybe the philosophy students in your congregation will understand the distinction, but for most folks the terminology will be unfamiliar.

Here's how I tried to explain the different categories in a recent sermon--

The disciples are human and being human means that in everyone there is a part that is willing, as in eager, excited, passionate.  It is ON and ready to fulfill Jesus’ requests.

But there’s this other part that is weak, sickly, fatigued, disabled.  It draws back from Jesus and falls backwards into temptation.

I’m not sure what to call these two competing parts.  Jesus calls them the spirit and the flesh, but we don’t think in those terms nowadays.  It’s not our bodies that sap our best intentions.  It’s more than skin deep.  It’s in our souls.  Our very nature.  

How are you going to explain the difference when you preach on the Gospel of Mark's version of this passage?

I appreciate the fact that in the Wesleyan tradition the physical body is believed to be a gift from God, and we are expected to be good stewards of this gift.  The fleshy body of skin, bones, organs, and blood is not sinful; it is not the source of sin.  It does not tempt the spirit.