We have studied the magnetization of the recently discovered heavy fermion superconductor UTe$_2$ up to 56 T in pulsed-magnetic fields. A first-order metamagnetic transition has been clearly observed at $H_{rm m}$ =34.9 T when the magnetic field $H$ is applied along the orthorhombic hard-magnetization $b$-axis. The transition has a critical end point at $sim$11 K and 34.8 T, where the first order transition terminates and changes into a crossover regime. Using the thermodynamic Maxwell relation, we have evaluated the field dependence of the Sommerfeld coefficient of the specific heat directly related to the superconducting pairing. From the analysis, we found a significant enhancement of the effective mass centered at $H_{rm m}$, which is reminiscent of the field-reentrant superconductivity of the ferromagnet URhGe in transverse fields. We discuss the origin of their field-robust superconductivity.
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