But CO2 is only a tiny proportion of the earth's atmosphere, say climate sceptics

A common argument made by global warming sceptics is that CO2 forms only a tiny fraction of the total atmosphere. Richard Lindzen says; "The total carbon dioxide in the atmosphere is only 4 hundredth of one percent (0.0004 of total atmosphere). The total increase by volume of carbon dioxide in the atmosphere in the last 150 years is only one hundredth of one percent (0.0001)".

OK.

One tablet of Buprenorphine amounts to 0.00000000035% of the total weight of the human body. But is still works as a powerful pain reliever.

From which we learn that it is not the absolute mass,  but the effect of the substance that matters.

It is an undeniable physical fact of physics that CO2 has heat trapping properties.
There are six factors which affect earth climate, of which, undeniably, one is the greenhouse effect.

It is established that we have significantly increased the greenhouse effect by increasing the concentration of CO2 by 41%.

It is impossible to explain temperatures since 1980 without factoring in this increased greenhouse effect. (See this graph).