Q.Why is my potted olive tree weeping sap?
The Olive tree I have is in a pot in the kitchen, it gets plenty of light and water. However, it is leaking sap and getting everything under its branches sticky. In some places the sap type substance has built up and is forming stalagmites on branches, leaves, and the edge of the pot. It also has little brown nodules on some branches and leaves. I have pictures this time, sorry to re-post.
You have a Scale infestation and the sticky substance is Honeydew; the residue from the pests.
Treat with Neem Oil.
https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm
https://www.gardeningknowhow.com/plant-problems/pests/insects/control-plant-scale.htm