It’s amazing how many people will post detailed answers to questions that they clearly do not know the actual answer to.
The F-35, AKA “Fat Amy”, is “fat” for the simple reason that the F-35B VTOL exists:

VTOL aircraft require a number of design features, one of which is having only a single engine. All VTOL jets use a single engine because they require a series of thrusters and vents around that single engine to create vertical thrust. Having twin engines would be impractical.

The Harrier, undoubtedly the most famous VTOL jet, is often mistaken for being twin engined because of its dual intakes. Like the F-35, it’s also a chonky monkey.
Any other jet that is the size and weight of the F-35 would be built with twin engines. This is why all the other 5th gen jets of the same size or larger employ twin engines: F-22, Su-57, KAAN, KF-21, J-20, J-35 etc. The only other stealth fighter to employ a single engine is the Su-75, which is a light fighter, comparable to the F-16.
Generally speaking, single engine design are for:
- Light fighters like the F-16, J-10 etc.
- VTOL
Twin engine designs are for:
- Medium and heavy fighters (F-35 would be considered a medium fighter)
- Bombers or other long-range jets like spy planes
Sure, the F-35A and C models are not VTOL, but the whole idea was to make the three variants as cross compatible as possible. So having the A and C be twin engined while the B is single engine would not comply with this cross-compatibility design goal.
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The Korean KF-21, AKA “Korean Amy” is the best proof of this. The Koreans do not have a VTOL requirement, so their KF-21 uses twin engines. Keep in mind, the KF-21 is produced with the help of the F-35 design team:

The Korean KF-21 is what the F-35 would be if it didn’t have a VTOL requirement. Thus it has twin engines and isn’t nearly as “fat”.

The Turkish KAAN is also “F-35 adjacent” and uses a twin engine

The J-35, which all Western experts insist is a copy of the F-35 despite it being no more or less similar to the F-35 than the KAAN or KF-21, is also twin engined.
The major cost of an aircraft is not in the shape of the aircraft. The major cost is the avionics of the craft. American warcraft focus on survivability and attack potential. The F-35 has stealth qualities and outstanding avionics to avoid being struck by incoming missiles but has systems to fire over the horizon successfully on enemy craft. The missile technology and interface with the craft is far superior on the American craft. This technology all costs money.
F-35

SU-57
