Grasping inhomogeneous objects in real-world applications remains a challenging task due to the unknown physical properties such as mass distribution and coefficient of friction. In this study, we propose a meta-learning algorithm called ConDex, which incorporates Conditional Neural Processes (CNP) with DexNet-2.0 to autonomously discern the underlying physical properties of objects using depth images. ConDex efficiently acquires physical embeddings from limited trials, enabling precise grasping point estimation. Furthermore, ConDex is capable of updating the predicted grasping quality iteratively from new trials in an online fashion. To the best of our knowledge, we are the first who generate two object datasets focusing on inhomogeneous physical properties with varying mass distributions and friction coefficients. Extensive evaluations in simulation demonstrate ConDex's superior performance over DexNet-2.0 and existing meta-learning-based grasping pipelines. Furthermore, ConDex shows robust generalization to previously unseen real-world objects despite training solely in the simulation. The synthetic and real-world datasets will be published as well.