The protocol overhead of MQTT is extremely small, the smallest packet has only 2 bytes overhead. The payload-to-overhead ratio is typically extremely good. It’s also a binary protocol which reduces the overhead on the wire a lot.
An older but good blog post about the lightweightness can be found here: stephendnicholas.com/archives/1217
If you are interested in protocol details, check out this extensive blog post series: www.hivemq.com/mqtt-essentials-wrap-up/
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