Which specific model of lens is it? They made several revisions of the base lens, in addition to the L series model.
I would suspect the issue is the lens, and I'm curious to see what those who are familiar with the lens will have to say.
Light falloff in a zoom lens is not unusual, and it is one of the issues that the concept of "T-Stop" designed lenses are intended to address. In a mathematically perfect lens f/8 at 28mm will put the same amount of light per square inch on your film as f/8 at 80mm does, however it is not uncommon in lens design for this to fail slightly, and for longer focal lengths to lose a little more than expected and be darker. Additionally some zoom lenses may lose more/less light in the corners depending on what focal length you set them to, but I'm not familiar enough with Canon's film bodies and the metering systems used in them to comment much on what that may be able to do to the readings.
Depending on design, things like excessive dust on elements may make the issue worse. (If you have a patch of something disrupting the light path, and you 'zoom in', that disruption may now make up a greater percentage of the lens surface.) So it is worth taking a careful look at the lens to make sure you're not getting some delamination or something.
In general I chalk things like that up to equipment quirks, and just try to keep them in mind when shooting so that I can apply manual corrections. The important thing in my mind is whether or not the difference is consistent. Consistent errors can be corrected for easily enough with care and attention, it is the inconsistent errors that are a real pain.
Side note on testing lenses for cameras like an EOS - Since they're compatible with dSLRs as well, they can appear easy to test with one for some issues like this, however do remember to check for auto-adjustment profiles! Some brightness oddities are readily smoothed out during post processing in ways that aren't easy to accomplish in a film to paper workflow. That, combined with the ease of overlooking crop sensors, make for easily missed gotchas any user who might be coming over to explore film should keep in mind.