Weld defect detection is crucial for ensuring the safety and reliability of piping systems in the oil and gas industry, especially in challenging marine and offshore environments. Traditional non-destructive testing (NDT) methods often fail to detect subtle or internal defects, leading to potential failures and costly downtime. Furthermore, existing neural network-based approaches for defect classification frequently rely on arbitrarily selected pretrained architectures and lack interpretability, raising safety concerns for deployment. To address these challenges, this paper introduces ``Adapt-WeldNet", an adaptive framework for welding defect detection that systematically evaluates various pre-trained architectures, transfer learning strategies, and adaptive optimizers to identify the best-performing model and hyperparameters, optimizing defect detection and providing actionable insights. Additionally, a novel Defect Detection Interpretability Analysis (DDIA) framework is proposed to enhance system transparency. DDIA employs Explainable AI (XAI) techniques, such as Grad-CAM and LIME, alongside domain-specific evaluations validated by certified ASNT NDE Level II professionals. Incorporating a Human-in-the-Loop (HITL) approach and aligning with the principles of Trustworthy AI, DDIA ensures the reliability, fairness, and accountability of the defect detection system, fostering confidence in automated decisions through expert validation. By improving both performance and interpretability, this work enhances trust, safety, and reliability in welding defect detection systems, supporting critical operations in offshore and marine environments.