The growth in many countries of the population in need of healthcare and with reduced mobility in many countries shows the demand for the development of assistive technologies to cater for this public, especially when they require home treatment after being discharged from the hospital. To this end, interactive applications on mobile devices are often integrated into intelligent environments. Such environments usually have limited resources, which are not capable of processing great volumes of data and can expend much energy due to devices being in communication to a cloud. Some approaches have tried to minimize these problems by using fog microdatacenter networks to provide high computational capabilities. However, full outsourcing of the data analysis to a microfog can generate a reduced level of accuracy and adaptability. In this work, we propose a healthcare system that uses data offloading to increase performance in an IoT-based microfog, providing resources and improving health monitoring. The main challenge of the proposed system is to provide high data processing with low latency in an environment with limited resources. Therefore, the main contribution of this work is to design an offloading algorithm to ensure resource provision in a microfog and synchronize the complexity of data processing through a healthcare environment architecture. We validated and evaluated the system using two interactive applications of individualized monitoring: (1) recognition of people using images and (2) fall detection using the combination of sensors (accelerometer and gyroscope) on a smartwatch and smartphone. Our system improves by 54% and 15% on the processing time of the user recognition and Fall Decision applications, respectively. In addition, it showed promising results, notably (a) high accuracy in identifying individuals, as well as detecting their mobility; and (b) efficiency when implemented in devices with scarce resources.