In conventional 3D printing, the layer-by-layer approach leads to mechanical weaknesses, particularly in the vertical tensile strength (Z-axis) and the shear resistance between layers. To address this, our study introduces a novel non-planar toolpath planning framework for 3-axis printers, named WeaveX, inspired by nature. This method involves moving the nozzle in the XY plane while periodically adjusting its height in the Z-axis, enhancing interlayer bonding and shear resistance. We developed two distinct toolpath designs: Scheme 1, which varies layer thickness, and Scheme 2, which maintains a consistent layer thickness. These designs were closely examined to understand their impact on toolpath width and layer thickness, considering various parameters. Both schemes resulted in "dumbbell"-shaped toolpath geometries, a characteristic that can be lessened by reducing print speed. Mechanical tests revealed that objects printed using these schemes significantly outperform traditional planar toolpath methods in terms of mechanical strength, showing improvements of 31.9% and 67.5% in interlayer shear resistance. Notably, these new strategies can be combined with each other or with conventional methods, broadening their potential applications.