Caloric Test: What defines bilateral caloric weakness?

The answer here depends on the stimulus and recording parameters, and guidelines for these may vary e.g. between different regions. For this reason it is often recommended that vestibular clinics gather their own normative data.  The British Society of Audiology guidelines indicate a value of < 8 º / sec for all 4 irrigations as indicative of bilateral weakness (BSA 2010) whereas another commonly used criteria is that the total response should be 20 °/sec or greater. Zapala et al (2008) present an extensive literature review of the ranges shown in different studies, and provide a description based on several thousand cases with caloric response data.

Please note that the law of large numbers applies when considering the interaural ratios (canal paresis and directional preponderance). The low overall numbers in a case of bilateral caloric weakness make these ratios unstable so should be ignored when this is the case. 

References and caveats
Zapala, D.D., Olsholt, K.F., and Lundy, L.B. (2008) A comparison of water and air caloric responses and their ability to distinguish between patients with normal and impaired ears. Ear and Hearing 29 (4) pages 585-600.