One of mine does this as well.. My girlfriend and I recently purchased 2 juvenile beardies yesterday (neither of us has had one before). We were told they grew up together and would be compatible with each other.. We still don't know their sex, but I assume one is male and one is female.. We currently have them in the same housing and figured that once they start getting bigger, we'd either buy 2 new tanks, or just another tank and split them up. She's concerned and doesn't want to split them up... Me on the other hand has read multiple stories about aggressiveness and harming/killing one another to be dominant. One was already bigger to begin with.. And already seems more "dominant" I fear that the smaller guy is not going to have the specific needs in order to grow. Other than that, there hasn't been any sort of hissing, biting, or even any behavior that implies any harm would be done.. It just seems as if the smaller guy/girl is a pushover and the bigger one is an ass. ?
They are solitary and can get aggressive with eachother as you said. For that reason, I would give them their own large enclosures so one doesn't dominate resources (food, basking spots, etc) or harm the other. If you're getting a new tank I'd just invest in large ones with proper lighting from the start. The most cost effective way to go is to build your own if you can, something along these lines. https://beardies.dreamwidth.org/2145.html