We evaluate the sink capacity of wireless code division multiple access (CDMA) sensor networks with layered architecture. We introduce a model of interference at a sink considering two kinds of interference: multiple access interference (MAI) and node interference (NI). We also investigate the activity of sensor nodes around the sink in relation to gathering data under a layered architecture. Based on the interference model and the activity of sensor nodes around the sink, we derive the failure probability of the transmission from a source node located one hop away from the sink using Gaussian approximation. Under the requirement of 1% failure probability of transmission, we determine the sink capacity, which is defined as the maximum number of concurrent sensor nodes located one hop away from the sink. We demonstrate that as the node activity of the MAI decreases, the variation of the sink capacity due to the node activity of the NI becomes more significant. The analysis results are verified through computer simulations.