We report combined experimental and theoretical analysis of superconductivity in CaK(Fe1−xNix)4As4 (CaK1144) for x=0, 0.017, and 0.034. To obtain the superfluid density ρ=[1+ΔλL(T)/λL(0)]−2, the temperature dependence of the London penetration depth ΔλL(T) was measured by using a tunnel-diode resonator (TDR) and the results agreed with the microwave coplanar resonator (MWR) with the small differences accounted for by considering a three orders of magnitude higher frequency of MWR. The absolute value of λL(T≪Tc)≈λL(0) was measured by using MWR, λL(5K)≈170±20 nm, which agreed well with the NV centers in diamond optical magnetometry that gave λL(5K)≈196±12 nm, which agreed well with the NV centers in diamond optical magnetometry that gave λL(5K)≈196±12 nm. The experimental results are analyzed within the Eliashberg theory, showing that the superconductivity of CaK1144 is well described by the nodeless s± order parameter and that upon Ni doping the interband interaction increases.