How does a fighter jet perform good and quick maneuvers with such small wings?
Fighter (combat) aircraft are designed to perform quick maneuvers in order to get into a position quickly to engage and shoot down an enemy aircraft or evade incoming threats (like missiles, etc.). Civil aircraft like airliners are designed with other things in mind like comfort, safety, reduced fuel consumption, etc.

The wings are only a part of the story in performing maneuvers like those performed in air combat maneuvering, which depends on a number of aircraft characteristics like,


Power - For carrying out most of the maneuvers (like wingover), the excess power available matters. Fighter aircraft have more excess power, which translates into more acceleration. That allows it it enter into maneuvers quickly compared to the civil aircraft. In case of emergencies, the combat aircraft can use their afterburners to gain significant extra power.
Thrust-to-Weight Ratio - Most of the modern fighters have high thrust-to-weight ratios, usually more than 1 (which allows them to accelerate in vertical climb). This allows the fighters to accelerate far faster compared to the civil aircraft. For example, F-15 (>1) had a thrust-to-weight ratio more the three times that of the Concorde (~0.33).




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Stability Most of the fighter aircraft today are designed to be unstable. This makes the aircraft respond to control inputs much more quickly compared to the airliners (which are usually not unstable in the roll axis). This means that the combat aircraft are capable of maneuvering much more quickly.
Inertia In case of large wings, the roll inertia is very high. This prevents them from performing quick maneuvers. Also, the damping of the large wings is also to be considered. In case of fighters, however, the short wings, having smaller inertia helps in achieving high roll rates.
Wing Loading The smaller the wing loading, the better the turn performance. Most of the combat aircraft employ a blended wing-fuselage design, that reduces the load on the wings. For example, the Eurofighter Typhoon (~300&nbsp;kg/$m^{2}$) has about half the wing loading of A380 (>600&nbsp;kg/$m^{2}$). In fact, an F-15 produced enough lift with half a wing gone to perform a successful landing.




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Control Surfaces- In general, the combat aircraft have more number of control surfaces like canards (in addition to primary control surfaces) compared to the civil aircraft. This enables the pilot to maneuver the aircraft much more quickly compared to airliners.




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Due to these reasons, the fighter aircraft are able to perform maneuvers much better and faster compared to airliners.