OK, the effect is low on Earth but what about Venus with 93 times more gas?

gamma = g/cp = g/839

since cp = 839 J/kg/K for CO2.

g on Venus, without correction for molecular motion is 8.87 m/s^2. Venus rotates so slowly that rotation will be negligible in determining g. On the other hand molecular motion could be higher than on Earth since temperature is higher but molecular mass is also higher. With a surface temperature of over 730 K the g force experienced by molecules will be

730 K CO2 has a v_rms = sqrt(3 R T/Mm) = sqrt(3*8.31*730/0.044) = 643 m/s

g = 8.87 - 2*v_rms^2/3r = 8.87 - 2 R T/Mm/r
g = 8.87 - 2*643^2/3/6051000 = 8.824

That is a 0.5% decrease. Not much there either.

On the Gas Giants one could assume that the heat gradient reaches one third of the cold value when temperature gets very high in the very deep atmosphere. On the other hand with a weaker adiabatic temperature gradient the temperature there won't increase that much with depth.

The lowest level the heat gradient can reach is when molecular speed is equal to free fall. Two thirds of the molecules will be like small satellites orbiting the planet. This will happen when the v_rms = sqrt(3 R T/Mm) = sqrt(g r)
= T = g r Mm/3/R

For Saturn, with almost only hydrogen in the atmosphere, this will happen (approximately, since gravitational acceleration will be lower deeper down in the atmosphere) when T = 10*60E6*0.001/3/8.31 = 24 000 K, and on Jupiter at T = 25*71500000*0.001/3/8.31 = 71700 K.
I have no idea if such high temperatures can exist in the gas phase or if those temperatures are assumed to be in the metallic hydrogen layers.

If there is something like adiabatic temperature gradients for liquids and solids the same effect should be there. For liquids there are and one could assume that for the Sun the weight of matter will only be 1/3 when the temperature has reached the T = g r Mm/3/R or equivalent for liquids.

It could also give some clue to as why there is an electric field in atmospheres. Imagine there is some degree of ionization. This will lead to free very light electrons that will have a very much higher speed than the ions. Electrons will thus be less affected by gravity, there will be polarization and thus a radial electric field.

David