It works for the Russian navy:
- Coastal corvette (Brig), 1100 t
- Corvette 20380, displacement 2220 tons,
- Frigate 22350, displacement 5400 t,
- Destroyer (Clipper), displacement 9000 tons,
- Cruiser, displacement 13500 t,
- Battleship, displacement 25,860 tons,
- Aircraft carrier, displacement 51720 tons.
The 1960s USN version had:
Ocean Escorts: ~4000tons, but 20knot Merchant Escorts, hence their "Destroyer Escort" numbering.
Patrol Frigate: 4100tons
Destroyers: ~4500tons for Charles F. Adams class
Destroyer Leaders (Spoken "Frigates"): ~8000tons
Cruisers: 15,000 tons or so.
Battleships: ~60,000tons for Iowa, the preceding South Dakota class was 45,000tons
Carriers: 93,000tons for USS Enterprise CVN-65, 82,000tons for Kitty Hawk class CV.
The reason for the relatively similar weights of the DEs, PFs, and DDGs is their range requirements. all were expected to go across the Atlantic, the difference is what their primary role was. DEs escorted merchant ships, while PFs and DDGs escorted carriers and amphib groups.
There is another scheme, but it needs improvement Air defense complex:
corvette - self-defense air defense (50 km)
frigate - medium-range (100 km)
destroyer - long-range (200 km)
cruiser - long-range (400 km) and anti-satellite
Not a bad measurement, but obviously makes no mention of size. Plus the US Mk41 VLS makes it very hard to apply today.
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As to what I think a "Frigate" means, I'm assuming a roughly 4500-7200ton ship (the new US Constellation class is HUGE but has to be since it's getting Aegis),
primarily focused on antisubmarine warfare with only enough SAMs to protect itself and maybe a small convoy of merchant ships. Even the Constellation-class only has 32cell Mk41 and 16x AShM in a separate launcher, not significantly more than the 4200ton FFG-7 class. Needs a helicopter and hangar, and if possible enough space for 2x SH-60 or equivalent. Aegis is not required, but is a "very nice to have" for a convoy escort. Problem is limited magazine capacity for SAMs, but I'd assume that there would be at least one CG or DDG with flag facilities per convoy, and no Tomahawks/equivalent in convoy escort VLS.