We report results from the Wide-orbit Exoplanet search with InfraRed Direct imaging, or WEIRD, a survey designed to search for Jupiter-like companions on very wide orbits (1000-5000 au) around young stars (<120 Myr) that are known members of moving groups in the solar neighborhood (<70 pc). Companions that share the same age, distance, and metallicity as their host while being on large enough orbits to be studied as isolated objects make prime targets for spectroscopic observations, and they are valuable benchmark objects for exoplanet atmosphere models. The search strategy is based on deep imaging in multiple bands across the near-infrared domain For all 177 objects of our sample, z(ab)', J, [3.6], and [4.5] images were obtained with CFHT/MegaCam, GEMINI/GMOS, CFHT/WIRCam, GEMINI/Flamingos-2, and Spitzer IIRAC. Using this set of four images per target, we searched for sources with red z(ab)' and [3.6]-[4.5] colors, typically reaching good completeness down to 2 M-J(up) companions, while going down to 1 M-J(up) for some targets, at separations of 1000-5000 au. The search yielded four candidate companions with the expected colors, but they were all rejected through follow-up proper motion observations. Our results constrain the occurrence of 1-13 M(J)(u)p planetary-mass companions on orbits with a semimajor axis between 1000 and 5000 au at less than 0.03, with a 95% confidence level.