It's often said that Canada has "weak" mayors. Technically, this is untrue.
Here's the short version: the term "weak mayor" is borrowed from the United States, where it refers to a very specific governance arrangement. In the US, there are two dominant forms of local government: mayor-council, and council-manager. They differ in a lot of ways, including with respect to the mayor. "Strong mayor" and "weak mayor" are variants of the mayor-council model, depending on the extent of executive authority vested in the mayor.
In Canada, we don't have the mayor-council form. We have the council-manager form. So, we don't have "strong" or "weak" mayors.
If you want to read the long version of this argument, have at it.
Often, people will say they want "strong mayors" without really understanding the term. What they mean is that they want the mayor to have more power. Well, I've got good news for you. See #8.