Hi Sheila
I don't think you have a problem with aviary size it's plenty big enough for two chips. I also don't think you're being over protective, fighting can be very serious, and lead to fatal actions. It would be helpful to know the history of these two, are they brothers, and have they always lived together? Did they come from a pet shop or a breeder?
I would not be too worried at this stage that Timmy is a different size, with mine there is quite a difference in their sizes, even those born on the same day. But from what you say so far there is a problem, with Sprite throwing his weight around a bit too much. Try to find out if they both end up in the same nestbox at night. This might seem odd, but even those that seem to hate each other during the day can often choose to spend the night together. What I think you have to judge is are they just sorting themselves out as to who is dominant, or is the fighting really bad and threatening Timmys' life. They all have squabbles, but a real fight means you need to take action. A real fight is when they roll around together in a furious ball, this is where ears get ripped and noses get bloodied. Squabbling is where one will snap at another but does not pursue a chase once the weaker one has moved away.
One other thing I have found, chipmunks like Timmy can completely change their personality once they have been separated from their aggressor. In the end of the day this is only a decision you can make from your own observations, but be prepared to have to make a decision to separate them, for the sake of Timmys' quality of life. I'm not saying you're there yet, as you have not had them that long, but keep a close eye on them, and see if you can work out what's going on, and let us know.