Hey there! Thanks for your support, glad to hear you're enjoying the game!
Alright, bear with me, Renown wasn't my strongest bit of writing here:
The way I see it, a low renown player is the lowest of the low - a nobody without any bearing on society at large. So, if such an individual were to commit a crime then they would have to face the full force of the law and a bounty to match. A high bounty player on the other hand is a celebrity of sorts - a mythical figure whose name is known far and wide. If this is their first time breaking the law, maybe their reputation softens the bounty on their head? Maybe the sheriff looks the other way and muddles the details of the crime? Conversely, if this isn't their first time committing a crime then what difference will a few hundred more on their bounty make really?