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The large scale reflector array of programmable metasurfaces is capable of increasing the power efficiency of backscatter communications via passive beamforming and thus has the potential to revolutionize the low-data-rate nature of backscatter communications. In this paper, we propose to design the power-efficient higher-order constellation and reflection pattern under the amplitude constraint brought by backscatter communications. For the constellation design, we adopt the amplitude and phase-shift keying (APSK) constellation and optimize the parameters of APSK such as ring number, ring radius, and inter-ring phase difference. Specifically, we derive closed-form solutions to the optimal ring radius and interring phase difference for an arbitrary modulation order in the decomposed subproblems. For the reflection pattern design, we propose to optimize the passive beamforming vector by solving a multi-objective optimization problem that maximizes reflection power and guarantees beam homogenization within the interested angle range. To solve the problem, we propose a constant-modulus power iteration method, which is proven to be monotonically increasing, to maximize the objective function in each iteration. Numerical results show that the proposed APSK constellation design and reflection pattern design outperform the existing modulation and beam pattern designs in programmable metasurface enabled backscatter communications.