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Reliable detection and accurate estimation of weak targets and their Doppler frequencies is a challenging problem in MIMO radar systems. Reflections from such targets are often overpowered by those from stronger nearby targets and clutter. Considering a 3-D data model where the coherent processing interval comprises multiple pulses, a novel weak target detection and estimation approach is proposed in this paper. The proposed method is based on creating partially overlapping spatial beams, and performing canonical correlation analysis (CCA) in the resulting beamspace. It is shown that if a target is present in the overlap sector, then its Doppler profile can be reliably estimated via beamspace CCA, even if hidden under much stronger interference from nearby targets and clutter. Numerical results are included to validate this theoretical claim, demonstrating that the proposed Beamspace Canonical Correlation (BCC) method yields considerable performance improvement over existing approaches.