We present the most sensitive 3 mm-survey to date of protoplanetary disks carried out in the Taurus-Auriga star forming region (average rms of about 0.3 mJy), using the IRAM PdBI. With our high detection rate of 17/19 we provide the first detections at wavelengths longer than about 1 mm for 12 sources. This enables us to statistically study the mm SED slopes and dust properties of faint disks and compare them to brighter disks using a uniform analysis method. With these new data and literature measurements at sub-millimeter and millimeter wavelengths, we analyze the dust properties of a sample of 21 isolated disks around T Tauri stars in the Taurus-Auriga star forming region. Together with the information about the disks' spatial extension from sub/mm-mm interferometric studies, we derive from the observed sub-mm/mm spectral energy distribution constraints on the dust opacity law at these wavelengths, using two-layer flared disk models and a self-consistent dust model that properly takes into account the variation of the dust opacity with grain growth. We find evidence for the presence of dust particles in the disk midplane that have grown to sizes as large as at least 1 millimeter in all the disks of our sample, confirming what was previously observed on smaller brighter objects. This indicates that the dust coagulation from ISM dust to mm-sized grains is a very fast process in protoplanetary disks, which appears to occur before a young stellar object enters the class II evolutionary stage. The amount of these large grains in the disk outer regions is also found to be stationary throughout the whole class II evolutionary stage, which indicates that mechanisms slowing down the dust inward migration play an important role in the Taurus-Auriga protoplanetary disks. Another result is that the spectral index between 1 and 3 mm for the six faintest disks in our sample is on average smaller than for the brighter disks, indicating either that these fainter yet unmapped disks are spatially much less extended than the brighter spatially resolved disks, or that fainter disks have typically larger dust grains in their outer regions. Considering that these fainter disks are more representative of the bulk of the disk population than the brighter ones, this may have important consequences for the theories of planetesimal formation and disk formation and evolution. Finally, we investigate the relations between the derived dust properties, namely dust mass and grain growth, and the properties of the central star, like its mass, age and mass accretion rate.