We have a weeping cherry in the middle of each of four boxwood beds and have had to replace them every few years. They grow well, then the bark begins to split and weep. We think it's due to borers and spray every spring but the problem continues.
Weeping Cherry Dying
Certified GKH Gardening Expert
This is a common tendency for Cherry Trees. It is called gummosis.
It is not a threatening problem.
If the bark is injured; this can be from weather and temperature changes or an injury to the bark since the bark is thin, it will ooze sap.
The tree can usually heal itself from this damage.
Prolonged wet conditions can be problematic.
Here are some links for you.