The compound EuCo2−yAs2 with the tetragonal ThCr2Si2 structure is known to contain Eu +2 ions with spin S = 7/2 that order below a temperature TN ≈ 47 K into an antiferromagnetic (AFM) proper helical structure with the ordered moments aligned in the tetragonal ab plane, perpendicular to the helix axis along the c axis, with no contribution from the Co atoms. Here we carry out a detailed investigation of the properties of single crystals. We consistently find about 5% vacancies on the Co site from energy-dispersive x-ray analysis and x-ray diffraction refinements. Enhanced ordered and effective moments of the Eu spins are found in most of our crystals. Electronic structure calculations indicate that the enhanced moments arise from polarization of the d bands, as occurs in ferromagnetic Gd metal. Electrical resistivity measurements indicate metallic behavior. The lowfield in-plane magnetic susceptibilities χ ab (T < TN) for several crystals are reported that are fitted well by unified molecular field theory (MFT), and the Eu-Eu exchange interactions Jij are extracted from the fits. High-field magnetization M data for magnetic fields H ab reveal what appears to be a first-order spin-flop transition followed at higher field by a second-order metamagnetic transition of unknown origin, and then by another second-order transition to the paramagnetic (PM) state. For H c, the magnetization shows only a second-order transition from the canted AFM to the PM state, as expected. The critical fields for the AFM to PM transition are in approximate agreement with the predictions of MFT. Heat capacity Cp measurements in zero and high H are reported. Phase diagrams for H c and H ab versus T are constructed from the high-field M (H, T ) and Cp(H, T ) measurements. The magnetic part Cmag(T, H = 0) of Cp(T, H = 0) is extracted and is fitted rather well below TN by MFT, although dynamic short-range AFM order is apparent in Cmag(T ) up to about 70 K, where the molar entropy attains its high-T limit of R ln 8.