Ising spin-orbit coupling (ISOC) can strongly protect superconductivity against exchange-field-induced depairing, typically leading to critical fields far exceeding the Pauli limit and continuous (second-order) phase transitions. Here, using a standard free-energy approach, we demonstrate that first-order transitions can emerge in superconductors with weak ISOC under large exchange fields. In this regime, theoretical approaches based on the gap equation fail to determine the thermodynamic critical field and instead yield only the supercooling field. We further identify two pronounced in-gap coherence peaks in the quasiparticle spectra, which represent the weak-ISOC manifestation of the previously reported mirage-gap states. These thermodynamic and spectroscopic signatures remain robust against modest impurity scattering and provide experimentally accessible criteria for identifying weak Ising superconductivity, which serves as an intermediate regime between conventional Pauli-limited and strong Ising superconductors.

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• First order phase transitions
• Spin-orbit coupling
• Superconducting gap
• Superconducting phase transition
• Low-temperature superconductors
• Noncentrosymmetric materials
• Superconductors
• Transition metal dichalcogenides
• Critical field