A quick question:

When atmospheric pressure is high (usually indicating warm weather) do helium balloons float better or worse when compared to low pressure (usually wet/changeable weather) conditions?

This is a for a minor detail in my novel.

short answer: I don't know

long answer:
I think you can apply Archimedes's principle, which says "a body immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid." so the upwards force on the balloon is
F = m g

g is about 10 and m is the mass of the air the balloon "displaces" which is equal to the volume of the balloon multiplied by the density of the air:
F = p V g

V is the volume of the balloon which we can assume is constant in both conditions, as is g, so that just leaves the density of the air p, which can be rewritten in terms of pressure and temperature using the ideal gas law:
p = MP/(RT)
= constant x P/T
F = another constant x P/T
(P is pressure measured in pascals and T temperature in kelvin)

so if you make up some values for the pressure and temperature you could work out how much bigger/smaller the upwards force will be for one condition compared to the other
F1 = P1/P2 x T2/T1 x F2
(I'm ignoring the downwards force of the weight of the balloon because its the same in both conditions)
If the temperatures were more or less the same then the balloon will float better with high pressure but I don't know if that would be the case, or what typical values would be for each weather condition

*note* I do not know anything about weather so you are probably better off consulting google - maybe try searching for info about hot air balloons or something?

Helium balloons float because they are lighter than air. To me, logically this wouldn't be affected by air pressure, so my instinctive reaction would be that they'd float at the same level, but be smaller under higher air pressure.

But as I say, that's an instinctive view, and what crazymat says does make sense, though I haven't looked through it in detail.

Well, I'm going to apply physics and logic to this as well. What that means is ignore everything I'm about to say, I'm thinking out-text and I guess only my conclusion matters.

The velocity of an object is affected by air resistance.

Higher atmospheric pressure would indicate that air particles are more compacted, making them closer together would logically add to the air resistance. At the same time, this would make the air more dense and thus the balloon, unless density is affected as well, would float better. Of course on that line of thought we could also say the effects would be proportional in either low or high pressure and thus it would negate itself and produce no change between the two.

In nearly all calculations I have done in physics, air resistance has been damn near negligible.

Conclusion I'm going to have to come to on this is that it would indeed float better in high pressure weather, but I would say the difference would be unnoticeable.

I had a thought for a way to test this. Rather than using an accelerometer or something like that which would be costly and probably make it so the balloon wouldn't even float...

Set up a balloon on each a high and low pressure day with a very long string. Record the length of string used and hold it lightly in your fingers or set up something that would be more consistent for friction on the string, a pulley or something, with two marks for beginning and end, time it. Of course you have to use the same volume of helium for each balloon. This will allow you to test it experimentally for the velocity at which it travels upwards.

Without being able to accurately gauge the amount of helium in each balloon I don't think that would work.

Right, my thoughts run like this:

Helium balloons float, as CMoose points out, because they are lighter than air
ES is on the right track with density
CMat brings in Archimedes, which I think is the right way to go

So helium specifically floats because the spacing of the molecules is wider than air, making it less dense.
The degree of lift that helium gives is relative to that physical ratio of helium density to air density.
If the air density increases (high pressure) then the balloon should float better because the physical ratio of densities has changed.
Does that sound reasonable?

The question perhaps should be whether high atmospheric pressure effects the balloon as well as the air.

A balloon containing helium molecules with the same spacing as "air molecules" would still float, because the molecules are physically lighter. Helium molecules having a relative weight of 8, and the average air particle (saying air is 75% N2, 20% O2, 5% CO2 for convenience) has a weight of 29.6.

So the amount of lift has more to do with it being lighter than air than it has to do with the density, as the density would be affected by the pressure. If the air pressure outside the balloon increases, the pressure inside must increase also, meaning the volume must decrease (assuming the temperature is constant). This would increase the density, but in line with the increase in density of the air.

So I still think it would float the same but be smaller.

I follow your logic, but I've just remembered something:

at a party last summer there were a load of helium balloons on a marquee. A very heavy thunderstorm came across and they all dropped, then when the storm had passed they started floating again.

So, judging by that, low pressure (storms) usually means that the balloons sink... Which I guess makes sense in my model of things, because the relative ratio from inside to outside the balloon is too slight for the helium to lift the weight of the balloon.

That's evidence I've seen, and it happened to every balloon at the party (the host was miffed because she'd spent a fair bit of money of them!) so I think it's accurate.

That brings in another factor - the potential stretch of a balloon. There will come a point at which the elasticity of the material prevents the density of the helium within from dropping as much as the air outside (otherwise you'd get some pretty formless and splodgey balloons) thus increasing the relative density of the gas within. Hence the decorative floaters being afraid of the thunder. Something like a weather ballon on the other hand is make to take this into account due to the low pressures experienced at the extreme altitudes that they are designed to reach.