"... the spirit may be willing but the physical body is weak.” (Mark 14:38)

Then he returned to find them sleeping; and said to Peter, “Simon, are you sleeping? Couldn’t you have kept watch for even an hour? Watch and pray that you won’t fall into temptation – the spirit may be willing but the physical body is weak.” (Mark 14:37-38)
In Matthew, the statement is virtually the same:
And he returned to the disciples to find them asleep. He said to Peter, “You couldn’t even keep watch for me for one hour? Watch out and pray that you will not be tempted – for the spirit may be willing but the physical body is weak." (Matt. 26:41)
In Luke, it states:
Then he asked them, “Why are you sleeping? Get up and pray that you won’t enter into temptation.” (Luke 22:46)

Why is Jesus saying this?

What does Jesus mean by this? Yes, there is the general guiding principle here, that praying can help keep us from falling into temptation. But why does Jesus say this at this particular time? Why are his students at risk of falling into temptation as Jesus goes off to pray?

Were they going to be tempted with women or fine foods? Perhaps they were going to be tempted by achieving fame somehow? That would be ridiculous, because they had gone to a remote garden in the middle of Mount Olive.

Or is Jesus just speaking about them sleeping? Is it that they were sleepy, and tempted to give up the watch and go to sleep?

Sleep is, after all, very tempting. Most of us can certainly fade off to sleep if we are tired. Many of us do this when we are being challenged. We feel sleepy because unconsciously we can forget about our daily troubles and go off into dreamland for a little bit.

In this way, sleep can be used as a form of escape. A way to avoid reality for a little while. We can escape into our dreamscape and forget about the hassles of our waking lives.

Jesus wanted them to keep watch. Why? He didn't want to be arrested while he was praying. His prayer was important to him. So he wanted some advance notice from his disciples.

In other words, he wanted some privacy while he was praying. Jesus was submitting himself to God in a humble way in his prayer. This is an intimate and confidential relationship between Jesus and God. Jesus didn't want this to be displayed to those who were coming to arrest him.

Jesus' prayer was a private thing. This is illustrated elsewhere:
In the morning he rose early before sunrise and went to a solitary place to pray. (Mark 1:35)

After he had sent them away, he departed to a mountain to pray. (Mark 6:46)
He also criticized the temple preachers for praying in public:
And have the important seats in the synagogues and the places of honor at the feasts – yet they forcibly appropriate widows’ households and for appearances’ sake offer lengthy prayers. They will receive the greatest consequences.” (Mark 12:39-40)
Jesus had a personal, private relationship with God. He held that relationship in the highest esteem. He didn't want his coming arrest to interfere in his relationship with God.

So his disciples were supposed to be standing guard. That is, unless they were tempted to fall asleep instead - which they did.

Why is the spirit 'willing'?

The disciples of Jesus wanted to follow Jesus' instruction and keep watch for him. They were 'willing' to do this because they saw themselves as Jesus' servants. They were his followers.

And falling asleep in this context would mean not following his instructions. Thus, they were tempted to sleep, as it was dark and they were undoubtedly tired. So in order to stay awake, they had to try hard to not sleep.

The 'spirit' that Jesus refers to is the spirit-person. This is the individual who drives the physical body - much as a car driver drives a car. After the death of this body, we leave it behind.

This spirit-person, is who we ultimately are. We are each spiritual entities. The feeling, willing person is separate than the physical body, which needs to sleep.

Why is the physical body weak?

The physical body is basically a complicated machine - not unlike a robot. But unlike a robot, we are the drivers of this machine.

Jesus states that the physical body is weak because if we leave everything up to the physical body - and do only what the body urges us to do - we will effectively become animals. The path of the spirit-person is to learn the difference between who we are and the physical body. Once we do this, we can direct our physical body, like a driver who directs a machine.

Without the direction of the spirit-person within, the body would simply live to eat, sleep and have sex. With our direction, we can redirect the senses and the body to help us grow spiritually.

Jesus was not making them sleep-deprived. They would have plenty of time to sleep after Jesus' arrest. It was just during that moment that Jesus wanted to make sure they stayed awake so he wouldn't be interrupted as he was praying.

Furthermore, Jesus' prayer was critical to what was going to happen. He was troubled about what was going to take place in the coming hours. So he reached out to God because he took refuge in God:
They left for a place called Gethsemane and he told his disciples, “Sit here until I have prayed.” He brought Peter, James and John with him, and became sad and troubled. (Mark 14:32-33)