I watched Babcock Socorro video and it looks great
The first thing to determine is if he wants something with or without a port system and how portable it needs to be.
Right now the only camera that is really small and does not need a port system is the Sony RX100. The Mark III and IV have a lens that is not really versed for macro but the Mark IV supports 4K though with some limitations.
If you are looking at something really portable and want maximum still versatility then the RX100 Mark II is the camera of choice
If instead you want 4K the choice is more difficult. If your priority is video I would seriously consider the Panasonic LX100 especially for wide angle.
However for still images the lack of pixels does show and the RX100 mark IV is a better choice.
Both cameras have limitations for macro and need something like the Nauticam CMC to reach frame widths between 32-36 mm
The canon G7X is a great little camera for stills but the battery life is too limited for video it still requires a port system to operate properly but once you have it works great both at wide angle and macro but all considered nothing that the older Sony RX100 Mark II can't give you.
So in summary if you don't need 4K grab a bargain on a Sony RX100 Mark II it takes great stills and HD video and is truly a small rig.
If you do need 4K and stills are a priority get a Sony RX100 Mark IV
If you are an avid video shooter and want 4K occasionally taking stills and you are more into wide angle (I see that your videos are caribbean mexico nothing super small) the LX100 is a good option although it is not really that small, the camera is not pocketable and the housing has a port system although with the short port it looks pretty compact.
If you are a macro fanatic looking for a 4K camera you need to look at a micro four third camera, the new GX8 housing has similar weigh to the LX100 and with kit lens and macro port 35 you can use it as a compact camera with wet lenses.
In terms of dimensions:
RX100 15 cm width 1.2 kg housing with camera
LX100 18 cm width 1.6 kg housing with camera and port
GX8 20 cm 1.6 kg housing with macro port 35 and 14-42 lens