…….It’s actually quite simple: pressure, pressure, pressure!
Champagne (and sparkling wines made in the méthode champenoise style) undergo a secondary fermentation within the bottle.
Taking into consideration that carbon dioxide is a byproduct of fermentation, the gas remains trapped within the bottle, hence the reason your wine sparkles.
This trapped gas needs a thicker, heavier vessel to withstand all that pressure caused by secondary fermentation. The classic Champagne-style bottle is similar to that of a Burgundy-style bottle, with slightly thin, slanting shoulders.