A few days ago I constructed a tape measure type antenna for 2 meters.
It is a 3 element beam and uses a hairpin or beta match.

Ran a return loss on it with the signal generator/spectrum analizer. The
best return loss was about 149 Mhz instead of 146. Thought it may be
because the tape AI used was 1/2 inch wide instead of 1 inch wide. I tried
lenghtning the hair pin form 5 inches to 6 inches. This did not change the
frequency of the return loss to any great ammount , but the RL went from
around 20 or more db to 10 db.

Did a little research on the hair pin match. From what I am getting out of
this, and it is very rough, is that the length of the driven element does
not make much differance in the actual resonate frequency of the antenna.
It is mostly where it is placed on the boom and the other elements that
determin the frequency of the antenna, but the length of the driven element
is determined by the impedance of the transmission line to be matched and
the impedance of the antenna/driven element.

Is that mostly correct or did I miss something in my reading ?

Hmmm. I think it's easier to look at it otherwise.

If you consider the driven element as a dipole in isolation, its
resonant frequency is going to be controlled by the length and the
width (thickness) of the element. Longer elements have lower resonant
frequencies, and for any specific length, thicker/wider elements will
have lower resonant frequencies. My guess is that using 1/2" tape
rather than 1" tape was what made the resonant point somewhat higher
than you had expected.

Adding the reflector and director elements is not going to change the
resonant frequency of the DE very much. What it will tend to do, is
change the radiation resistance (the resistive portion of the
impedance) and thus the impedance at the feedpoint. In a typical
Yagi, the feedpoint impedance is often down in the 25-ohm range.

What the hairpin-match for a Yagi does, is create an L-match which
raises the feedpoint impedance to 50 ohms, compared to what you would
have without such a match but with the DE cut for your desired
resonant frequency.

Starting with a DE length which is resonant, you shorten the DE
slightly. This changes the feedpoint impedance at your desired
resonant frequency from purely resistive (too low) to a slightly lower
resistance in series with a capacitance.

This R + jXc (series) is electrically equivalent to a parallel
combination of R' || jXc' where (in this case) R' is 50 ohms.

You then add a shunt inductance (the hairpin), which appears in
parallel to the capacitive reactance... when the magnitudes of the two
are equal, the combination appears as a very high impedance in
parallel with R' and all you're left with is R', or 50 ohms.

When you lengthened the hairpin, you added inductance... probably too
much, so you've not only cancelled out the capacitive reactance from
the DE, but have left some excess inductance shunted across the DE.
Hence, the reduced return loss. I would not expect this sort of tweak
to affect the resonant frequency, since that's a function of the DE
length and thickness.

So, in your case, what you would want to do is either lengthen the DE
slightly, or use wider measuring tape. Either would bring the DE's
resonant frequency downwards a few MHz. You would then use the
hairpin match (as designed) to bring the feedpoint impedance to 50
ohms. You could try adding a "capacity hat" out at each end of the
DE, which would have a similar effect... but given how difficult
measuring tape is to solder onto, that might be more hassle than just
cutting a new DE and installing it and then just trimming back a bit
at a time.

If you're going to be cutting and trying... you can tune the hairpin
inductance somewhat, without having to actually cut it repeatedly, by
opening and closing the hairpin "loop".