Driven by technological innovations and the increasing demand for smart manufacturing, the Industrial Internet of Things (IIoT) has undergone rapid development, becoming a pivotal force in the transformation of modern industrial processes. In smart manufacturing factories, a large number of heterogeneous devices generate tasks with varying degrees of delay sensitivity, which poses significant challenges to task offloading and resource allocation. However, existing studies on task offloading often overlook these differences, leading to inefficient resource allocation. To address this issue, this paper novelly constructs satisfaction of information (SoI) functions based on delay requirements of various tasks, so their specific offloading needs can be accurately quantified. Additionally, a joint optimization problem under the Device-to-Device (D2D)-Aided Multi-access Edge Computing (MEC) architecture, integrating task offloading with resource allocation to maximize the weighted SoI, is proposed. Afterwards, the optimization problem is transformed into a Markov Decision Process (MDP). Finally, a proximal policy optimization (PPO) based SoI-maximization task offloading and resource allocation (PASTA) algorithm is developed to solve the optimization problem. Simulation results demonstrate that our proposed scheme outperforms existing methods in handling delay-sensitive tasks and exhibits its superior practical applicability in diverse industrial scenarios.