This paper introduces a surface plasmon resonance (SPR) sensor using tapered silica fiber and photopolymer coating for enhanced refractive index (RI) detection. Tapering the silica fiber to a diameter of 10 µm ensures the evanescent wave leaks into a 1.8-µm thick photopolymer film, which increases the average waveguide RI and broadens the RI detection range accordingly. A 50-nm thick single-side gold film is coated on the photopolymer film, exciting SPR and causing less light transmission loss than a double-side gold film. The method avoids the complex microfabrication processes of conventional polymer optical fiber SPR sensors, while the waveguide RI can be controlled by altering the curing time of the photopolymer during fabrication. The sensor has an overall sensitivity of 3686.25 nm/RIU, enabling RI detection of 1.333 - 1.493. Moreover, the sensor has an ultrahigh sensitivity of 6422.9 nm/RIU in the RI range of 1.423 - 1.493. The temperature response is about 1.43 nm/°C at 20 - 50 °C, which has little impact on RI detection. Finally, we demonstrate that the sensor can grade the severity of hepatic steatosis by measuring the RIs of cytoplasm/triglyceride emulsions with superior sensing performance.