What s Sony s equivalent to Canon s Center Weighted Average Metering mode?

"Average" and "Center-Weighted" are basically the SAME, just as Multi-Segmented and Matrix are, likewise, equivalent to one another ("A rose by any other name..."). IF you read your camera's Instructions Manual, you'll discover which is more suitable to your style of shooting; you'll also discover when to use the other shooting modes for best photo-taking experiences, which varies from one situation to another. And you'll learn how to overcome difficult lighting situations, too. The "best" shooting mode is WHEN it is appropriate to use the selected mode for the appropriate situation; each mode has its advantages for the appropriateness of the situation at hand, and disadvantages when not used in the appropriate shooting situation. HOW will you know when a shooting mode is "appropriate"? READ the camera's Instructions Manual and find out. I'm not being cruel or mean; I'm being totally honest. The quality of your photos are totally comparable to your knowledge (you acquire) and skills (you develop); the camera is only a tool that will render images in accordance to or at the level of what you know about using said camera's features, functions and options. The more you learn and practice, the better images that will result. Good luck and best wishes.

The standard set of metering modes contains three options - multi-segment, center-weighted, and spot. Different brands may call it slightly differently and may add one or two more modes but essentially they just go around those three. Unless you find one of those additional modes really helpful to your shooting, you should survive with just one or two of the standards. I for one stick to spot, all the time, since film.

In some cases there may not Be a reasonable equivalent.

Personally, I only use spot and multi-segmenting metering. I never use center-weighted metering.

Different Sony cameras have different metering modes - mine certainly has a center weighted metering mode!

My Sony has Multi Segment, Centre-Weighted, and Spot with Zone Area.

The obvious choice would be center-weighted.