In IoT-based smart healthcare services, the heterogeneity of connected wearable sensing devices open up a wide opportunity to develop various healthcare services. However, it also poses an interoperability challenge since each sensing device and application may have different communication mechanisms. Considering that challenge, web platform can be seen as a promising candidate for providing an interoperability layer as we can abstract various devices as single representation i.e. web resource. In this paper, we propose the design of middleware for enabling efficient web of things access over healthcare wearable devices. The proposed middleware consists of three components: gateway-to-cloud device, messaging service and data access interface. The gateway-to-cloud device has a role to perform low level sensor data collection from various wearable sensing device through bluetooth low energy (BLE) communication protocol. Collected data are then relayed to the cloud IoT platform using a lightweight MQTT messaging protocol. In order to provide device abstraction along with access to the stored data, the system offers two kind of interfaces: the Restful HTTP identified by unique universal resource locator (URL) for batch access and MQTT websocket interface identified by unique topic to accommodate access on sensing data in near real time stream manner.