Because E=MC^2 a very tiny, virtually unmeasuraable amount of matter is converted into energy during any energy exchange. In this case the weight of the burned wood is carried off by rising heat in the form of steam and that (H2O) is a major component of wood, yes, even dried (seasoned) wood. The chemical bonds give way to heat and realign as CO2 and various other compounds, the major element being Carbon. If you were to perform an experiement where the burning took place in a sealed glass box resting on a scale you would see that the weight remains unchanged, undetecable.

C^2 is such a vast number that the Hiroshima class atomic bomb annihilated only about 2 grams of matter. The rest was converted into other elements or was vaporized and became the deadly constituent of fallout. The sun is 864, 484 miles in diameter which means an incredible amount of mass is present. In its profligate expenditure of energy it converts about 4 million tons of mass into energy every second. In the solar arena at the distance of Earth, we are struck by the tiniest fraction of the total energy released but that energy, mostly in the form of heat, powers our global climate. If I remember right it averages about 3.2 calories per square centimeter per second.

If you want to do the math yourself, I've given you the Sun's diameter; the Earth is 8,000 miles in diameter (rounded up a few) at an average distance from the Sun of 93,000,000 miles. For ease call it 100 million. The speed of light is 187,262 miles per second. You will need a lot of paper when you square that. Best to use scientific notation.

The Sun will continue to convert mass to energy for another estimated 8 billion years before noticable changes begin to take place but that is another story.