Using Very Large Telescope/Spectrograph for INtegral Field Observation in the Near-Infrared (VLT/SINFONI), we have obtained repeated adaptive-optics assisted, near-infrared spectroscopy of the three central WN6ha stars in the core of the very young (~1 Myr), massive and dense Galactic cluster NGC 3603. One of these stars, NGC 3603-A1, is a known 3.77 d, double-eclipsing binary, while another one, NGC 3603-C, is one of the brightest X-ray sources among all known Galactic WR stars, which usually is a strong indication for binarity. Our study reveals that star C is indeed an 8.9-d binary, although only the WN6ha component is visible in our spectra; therefore, we temporarily classify star C as an SB1 system. A1, on the other hand, is found to consist of two emission-line stars of similar, but not necessarily of identical spectral type, which can be followed over most the orbit. Using radial velocities for both components and the previously known inclination angle of the system, we are able to derive absolute masses for both stars in A1. We find M1 = (116 +/- 31)Msolar for the primary and M2 = (89 +/- 16)Msolar for the secondary component of A1. While uncertainties are large, A1 is intrinsically half a magnitude brighter than WR20a, the current record holder with 83 and 82 Msolar, respectively; therefore, it is likely that the primary in A1 is indeed the most massive star weighed so far.