Hello Lawrence,

What you are describing and what I see in your images- a red, amber, or reddish jelly-like sap oozing from a weeping cherry- is most often called gummosis. Gummosis is not a disease itself. It is the tree's response to stress, injury, insects, or infection.

For ornamental cherries in Michigan, the most common underlying causes are:

Bacterial canker (Pseudomonas syringae), a very common disease of cherries in cool, wet spring climates like Michigan. Symptoms include gummy sap oozing from branches or the trunk, sunken bark areas, and branch dieback.

Cytospora or other canker diseases, which create dead areas in the bark and cause amber-to-reddish gum to exude.

Physical injury or winter damage, such as sunscald, frost cracks, mower/trimmer damage, or pruning wounds. Cherries frequently respond by producing gum.

Borers or other insects. If the gum contains sawdust-like material (frass), boring insects become more likely.

How to determine which one it is:
Look closely at the area where the gum is emerging:
Sunken, dark, dead bark around the ooze → likely canker disease.
Gum mixed with sawdust or wood particles → likely borers.
Gum around a crack, pruning cut, or wound → injury or winter damage.
Dead twigs or branches above the oozing area →bacterial canker becomes more likely.

Treatment
Unfortunately, no spray cures existing cankers on ornamental cherries. Management focuses on reducing stress and removing infected wood.

Recommended actions:
Prune out dead or infected branches during dry weather.
Cut several inches below visible symptoms.
Disinfect pruning tools between cuts with alcohol or a bleach solution.
Avoid trunk injuries from string trimmers and mowers.
Water during drought but avoid constantly wet soil.
Do not over-fertilize with nitrogen. Excessive nitrogen can increase stress-related gummosis.

For Michigan cherries, MSU Extension notes that copper sprays are sometimes used preventively for bacterial canker, but timing is critical, and they are primarily preventive rather than curative.

My suspicion

Because you are in Oakland County, Michigan, and if this is a mature ornamental weeping cherry with red gummy ooze coming from the trunk or major limbs, my first suspicion would be bacterial canker or another canker disease, especially if there is any branch dieback. Those are extremely common on cherries in the Great Lakes region.

Sources at the links below:

Cherry: Gumming (Gummosis) | Hortsense | Washington State University

Gummosis of Fruit Trees

Early season bacterial canker management in cherry - MSU Extension

Managing bacterial canker in sweet cherries: What are the options? - MSU Extension

Bacterial Canker – Wisconsin Horticulture

Cherry: Bacterial canker | Hortsense | Washington State University

Gummosis | Yard and Garden 

I hope this helps!