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We consider the chaotic motion of low-mass bodies in two-body high-order mean-motion resonances with planets in model planetary systems, and analytically estimate the Lyapunov and diffusion timescales of the motion in multiplets of interacting subresonances corresponding to the mean-motion resonances. We show that the densely distributed (though not overlapping) high-order mean-motion resonances, when certain conditions on the planetary system parameters are satisfied, may produce extended planetary chaotic zones -- "zones of weak chaotization," -- much broader than the well-known planetary connected chaotic zone, the Wisdom gap. This extended planetary chaotic zone covers the orbital range between the 2/1 and 1/1 resonances with the planet. On the other hand, the orbital space inner (closer to the host star) with respect to the 2/1 resonance location is essentially long-term stable. This difference arises because the adiabaticity parameter of subresonance multiplets specifically depends on the particle's orbit size. The revealed effect may control the structure of planetesimal disks in planetary systems: the orbital zone between the 2/1 and 1/1 resonances with a planet should be normally free from low-mass material (only that occasionally captured in the first-order 3/2 or 4/3 resonances may survive); whereas any low-mass population inner to the 2/1 resonance location should be normally long-lived (if not perturbed by secular resonances, which we do not consider in this study).