How to determine if a wall wart is a regulated power supply

I was using my MM to examine several wall warts, and from what I’ve read about non regulated power supplies, they usually show a few volts higher on a MM than what the label says and regulated ones are much closer to the reported value. I also noticed that heavier wall warts I examined reported higher values, usually by a couple of volts. Are regulated wall warts usually lighter than non regulated transformers?

I took a wall wart from an old D-Link router and measured DC voltage which showed 5.187V consistently, and is much lighter than the ones reporting a higher voltage of similar size. Next, I tried to calculate the ripple percentage; I measured AC voltage and it showed 3.7mv. Using the formula:

Percentage Ripple = (output AC component/Output DC Component) * 100 = 0.071%.

Is it safe to say this is a regulated power supply?

Is connecting this power supply to the breadboard rails and then connecting the rails to VIN and GND equivalent to connecting the PS to VIN and GND and 5V and GND to the rails? I ask this because I’ve noticed that the 5V pin sometimes shows less than 5V, and I have a component which requires 5V±0.1

If a power supply is regulated, the output voltage will not drop significantly if you connect it to a load that is within the power supply output rating.

Older, transformer supplies are usually not regulated, and are used to power devices that have internal voltage regulation.

Are regulated wall warts usually lighter than non regulated transformers?

Yes.

Is it safe to say this is a regulated power supply?

Yes.

Is connecting this power supply to the breadboard rails and then connecting the rails to VIN and GND equivalent to connecting the PS to VIN and GND and 5V and GND to the rails?

Depending on the sort of Arduino the pin labeled Vin can change. In a Uno Vin must be at least 6.5V to allow the regulator to generate 5V.

I have a component which requires 5V±0.1

What components are these? If this is true then they should not be used with a micro controller system, nothing is guaranteed to produce this. Is this their power supply requirements? If so you must build and adjust a regulator especially for them.