Ncunceo, what kind of bar are you using? I've never heard of the diameter getting bigger as the weight increases. My gym has 35 and 45# bars (the kind you add weight plates to) and both sizes are the same diameter. EZ curl bars also use plates but have a smaller diameter (but are all the same size). The gym also has preloaded bars from 15 to 90 pounds that are the same diameter, regardless of weight. What kind are you using? Perhaps your gym has an alternative to the ones that change size?
I also have small hands and gloves are a big help in letting me grip bars. If those don't help, you might consider lifting straps but they won't work for every exercise.
I wish I had a better answer but I'm genuinely puzzled at the issue.

Sorry! Could you find a link to a photo showing what you're dealing with? Maybe if we could visualize, we could come up with an answer!