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Recently collaborative learning is widely applied to model sensitive data generated in Industrial IoT (IIoT). It enables a large number of devices to collectively train a global model by collaborating with a server while keeping the datasets on their respective premises. However, existing approaches are limited by high overheads and may also suffer from falsified aggregated results returned by a malicious server. Hence, we propose a Scalable, Privacy-preserving and veRIfiable collaboraTive lEarning (SPRITE) algorithm to train linear and logistic regression models for IIoT. We aim to reduce burden from resource-constrained IIoT devices and trust dependence on cloud by introducing fog as a middleware. SPRITE employs threshold secret sharing to guarantee privacy-preservation and robustness to IIoT device dropout whereas verifiable additive homomorphic secret sharing to ensure verifiability during model aggregation. We prove the security of SPRITE in an honest-but-curious setting where the cloud is untrustworthy. We validate SPRITE to be scalable and lightweight through theoretical overhead analysis and extensive testbed experimentation on an IIoT use-case with two real-world industrial datasets. For a large-scale industrial setup, SPRITE records 65% and 55% improved performance over its competitor for linear and logistic regressions respectively while reducing communication overhead for an IIoT device by 90%.