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I am constructing a small loop antenna; apprx 4' diameter, will be used with an antenna tuner and 100W transmitter, and hope to use it on 20m, 40m, and maybe other bands if possible. I can add a tuning capacitor to make it resonate on one of the bands but cannot help wondering... what does that get me?

Is a resonant antenna more efficient? I would assume so, but seem to recall that the increased efficiency is not really all that much.

The Question What is an antenna tuner? Why bother with resonant antennas in the first place? seems to address what I am asking, but the answer is still unclear.

Resonance or non-resonance does not have a direct effect on the efficiency or gain of the antenna. A resonant antenna is one that has only resistance without any reactance (capacitive or inductance) at its feedpoint.

To transfer the maximum available (or rated) power from a transmitter to its load (the antenna system in this case), the impedance of the antenna system must match the specified load impedance of the transmitter. Most transmitters specify a 50 ohm load without any reactance. If the antenna system has reactance (i.e. it is not resonant) the transmitter will not be able to put out its rated power. This is the primary reason we tend to try to "resonate" the antenna.

Imagine if transmitter manufacturers specified a 50 ohm resistive with 23 ohms of inductive reactance (50+j23) as the required load impedance. We would all be working to "non-resonate" our antenna systems to meet this specification in order to put out the rated power!

It is important to note that most antennas, even when resonant, do not have a 50 ohm impedance. It is therefore often required to add some type of matching network to the antenna system to transform the impedance to 50 ohms so that the transmitter can put out its rated power. The matching circuit may be designed to cancel out any reactance in addition to transforming the resistive component of the antenna system to 50 ohms.

As long as a near-conjugate match to the antenna feedpoint impedance is achieved, resonance and/or non-resonance doesn't matter at all. Let's assume we have antenna1 with 50 ohms of radiation resistance and no reactance at the feedpoint vs antenna2 with 100 ohms of radiation resistance and +j100 ohms of reactance at the feedpoint, (assuming negligible losses in the antenna).

For antenna1, we adjust our transmitter output to get 1.414 amps of current flowing through the 50 ohms radiation resistance. For antenna2, we adjust our antenna tuner to get 1.0 amps of current flowing through the 100 ohms of radiation resistance. Which antenna is more efficient and which will radiate the most power?

The power radiated by antenna1 is 50(1.414)^2 = 100 watts

The power radiated by antenna2 is 100(1.0)^2 = 100 watts

The power radiated by the resonant antenna1 is identical to the power radiated by the non-resonant antenna2. When are we going to lay that old XYL's tale to rest? The very basic purpose of an antenna tuner is to maximize the current flowing through the radiation resistance of the antenna. When it maximizes the current flowing through the radiation resistance of the antenna, it necessarily must accomplish a near-conjugate match not only at the antenna feedpoint but also at the transmitter output thus satisfying the maximum power transfer theorem's requirement of a conjugate match at every point in a conjugately matched system.

In a low-loss system, when we tune our antenna tuners for a 50 ohm Z0-match at the tuner input, we have tuned to a near conjugate match both at the tuner output AND also at the antenna feedpoint. The things that keeps those near conjugate matches from being perfect conjugate matches are the (hopefully) minor losses in the tuner and feedline.

I was shot down for saying this before, but.. at resonance you get the max gain. Also the antenna is purely resistive, current and voltage are in phase, you get the most power out of it. If an antenna is not resonant, it is not resistive, and you get voltage and current out of phase. You can introduce shift with additional components to get the antenna to look resistive again, and get the best signal power from it. But the gain will not be as in the ideal case. Some have pointed out it's not much, but anyone who ever got an RF burn when trimming and antenna and it peaked could argue against that.
Ultimately it will have less gain, the application determines if its acceptable or not.

EDIT

Despite all the negative feedback I still have to disagree with you all.
An antenna has resonance and bandwidth, in practice the antenna might not be resonant to a particular frequency, but the frequency falls within the bandwidth of the antenna and there's no noticeable decrease in performance.

However the effect becomes noticeable when you go outside the bandwidth. If it were true that resonance didn't play a role then you could use a 1cm antenna for 80m waves?? provided you had the appropriate matching network... clearly this isn't the case, just because the effect is not immediately noticeable in practice doesn't mean it's not there.

ref:
https://www.electronics-notes.com/articles/antennas-propagation/antenna-theory/resonance-bandwidth.php