I used to think that bounties represent the atrocity of someone's crime.
However, after some consideration, I believe a bounty equals someone's power. This includes someone's fighting potential, military power, etc. Or at least how accurately the Marines can determine it.
The most powerful individuals are given higher bounties because its where the strongest bounty hunters must focus their attention.
Examples:
Luffy's bounty after Arlong Park
Luffy got his first bounty because he attacked the Marine captain Nezumi.
However, Brannew put a bounty of 30 million on Luffy's head because he defeated the most notorious pirates in East Blue.
Luffy's bounty after Arabasta
Luffy disrupted the balance of the three great powers by defeating Crocodile, becoming a matter of subject even for the Gorosei. Despite the world-scale problem he caused, Luffy got a bounty of merely 100 million.
While 100 million seems little for someone strong enough to defeat a Shichibukai, it seems this amount was not far from Luffy's real fighting ability considering how outclassed he was during the war at Marineford.
Luffy's bounty after Ennies Lobby
Luffy learned how to use Gear Second, which vastly increased his fighting strength. His bounty was increased to 300 million.
Luffy's bounty not increasing
Despite defeating Gecko Moriah, attacking a Tenryuubito and destroying a Pacifista, Luffy bounty did not increase. This is because they did not believe his strength changed.
Luffy's bounty after Whole Cake Island
While Luffy performed no crime against the World Government, by conquering a victory at Big Mom's territory, and defeating two of her commanders, Luffy's bounty increased to 1.5 billion.
This is a clear example of how a bounty is closely related to your fighting ability.
Shichibukai bounties
After the Shichibukai system was abandoned, Brannew said they should give them new bounties, despite them being allies to the World Government until then, and technically nothing they did was considered a crime.
Yonko commander's bounties
According to the author, commanders like Katakuri have immense bounties because they act along with their captains, similar to how most Strawhats were given an increase of 50 million after the Dressrosa arc.
Their bounties seem incredible large, with someone like Queen having a bounty of 1.36 billion. In comparison, strong individuals like Jinbe or Eustass Kidd are on the 400 million range. However, I believe the commanders bounties, without the influence of their captains, would not have so much more.
Sum of bounties
According to Brannew, it seems that combining the bounties of two individuals can predict their combined strength too. He pointed out that while no pirate has a bounty surpassing Roger or Whitebeard, Kaido and Big Mom combined bounties are far superior.
New World bounties
It seems hard to believe that Pekoms, Tamago, Pedro, Perosperos and others all did something worse than the attack on Ennies Lobby to deserve a bounty higher than Luffy received after the incident.
However, they are all superior in strength than Luffy was around the time.
Regarding Nico Robin bounty
Robin's bounty is commonly used as an example of how a bounty doesn't equal someone's strength. This includes Aokiji's statement that it also represents someone's threat to the world government.
However, Aokiji words should be read between the lines. The government fabricated a story about Nico Robin destroyed six Marine battleships, to justify a bounty this high.
This means that, normally, a bounty this high would only belong to someone with some feat to justify it.