I know the proper way to put on your gi is to put the left side over the right side, but why is this? Where did this custom come from? I think it applies to all martial arts (at least I know it does for Aikido, Karate and Judo) or are there any exceptions?
Gi, or more properly dōgi (道着) is wafuku (和服), or Japanese Clothing, and the handedness (for lack of a better word) of kimono is that it is worn with the left panel over the right. It is mostly out of tradition, likely with roots in the the codification of Shintō traditions in which an order of things must be observed (for instance, when praying at a Shintō shrine, one washes their left hand first). This however is a guess based upon when we start to see the adoption of the left-over-right dressing correlating dates of Shintō's codification. As has been mentioned, in those occasions in which the body in a modern funeral is dressed in wafuku, the right panel is placed over the left.
Prior to the Heian period, we see a much larger variation in the styles of dress:
During the Nara period, the tradition was to wear a form of proto-kimono which overlapped right over left.
The modern kimono as a style of dress came into fashion during the Heian period, at which point it was adopted out of convenience and ease of construction (the tailor no longer needed concern himself with the shape of the body wearing the garment).
There are periods, as well, within the history of Japan in which the style of clothing has been controlled by law. For instance, government officials in the Meiji era were required to wear yofuku (Western Clothing) to official events. Sumptuary laws in the Edo period required the ostentatious colors of the Heian period to be forsaken for subdued colors (so that the wealthier merchant class would not upstage the less wealthy but higher caste Samurai), which lead to brocade being added to clothing as a means of displaying wealth.
Therefore, in answer to your question of "Why do we overlap left over right?", the answer is simple: Tradition. It's the same reason that we may bow to a kamidana, or that we do not wear shoes inside the dojo.
I seem to have been thaught a story similar to what Sardathrion explains, yet slightly different. Sadly, though, I have no reference other than "my sensei told me".
According to my sensei, people wore the left side on top because the inside of the kimono became easily accessible with the right hand, a bit like a big pocket, allowing to dissimulate weapons (most likely a tanto, or short knife) or carry small fans (which were popular in high society).
When someone died, they no longer needed to carry/hide weapons, at least not on this side anymore (I will admit I am not familiar with the traditionnal japanese afterlife). This is why, still according to my sensei, one would be buried with the right side over.
Origin of keikogi, and Japanese left-over-right dress tradition
The uniforms of karate, aikido, kendo, Brazilian Jiu-Jitsu, sambo etc are derived from the uniforms of judo, which were themselves based off of everyday Japanese clothing. As such, the tradition of wearing keikogi jackets left-side over right was likewise adopted from the traditional way to wear clothes generally. This tradition, like many Japanese cultural artefacts, was imported from China:
The Yо̄rо̄ Clothing Code of 718 marked a high point of Chinese-influenced politics for the early Japanese state.
The code specified that all robes should be crossed left side over right in Chinese fashion. Such "sidedness" of clothing is important in many cultures. Precisely because of the natural arbitrariness of left and right, sides can be used to express cultural differences of great import. A garment's sidedness is not something to be reversed lightly. The Chinese considered right-over-left a mark of barbarism. This explains the Japanese decision to abandon their traditional mode. All Japanese robes, including kimono, have wrapped left over right since the Yо̄rо̄ Clothing Code demanded it.
- Kimono: Fashioning Culture, Liza Dalby
Being civilised in the eighth century meant being like the Chinese... Following the relocation of the Japanese Imperial Court to Nara in 710, many other Chinese-instituted reforms took place, including the adoption of the courtly dress code, which was sanctioned by the Tang dynasty. Significantly, the Yoro Clothing Code, instituted in 718, stipulated that all robes be overlapped frontally from left to right in typical Chinese fashion.
8. Izutsu, Nihon josei fukushokushi, 31. See discussion of the Yoro Clothing Code, the Yoro ritsuryо̄, 31.
- The Kimono Inspiration: Art and Art-to-wear in America (Part 3) The Textile Museum, Washington D.C.
Other keikogi variations
Whilst most Japanese-related martial arts still use a style of gi not substantially different from the 1907 judo design, some have notably redesigned the jacket:
Taekwondo's dobok (cf. "dōgi"). While traditionally was modelled after the Japanese judogi, a newer ITDF style modelled after the traditional Korean dress hanbok (with a closed v-neck jecket) is now common.
Sambo's kurtka has epilettes and belt loops.
It may be something akin to button sides. This may explain the difference in death as well, as few corpses dress themselves.
Mens’ buttons are on the right side because men have always tended to dress themselves and most men (and women, for that matter) are right-handed. Womens’ buttons are on the left side because years ago (say, during the Victorian Era), the women that could afford fancy clothing with a bunch of buttons would rely on maids to help dress them.
- Why Do Men’s and Women’s Shirts Button on Different Sides? (primermagazine.com)
As a righty, I know I find it easier to tie the left side first as the whole top is less secure and my right hand is in a more comfortable position to do the tie, while the second tie (left over right) my left hand is now on point and it's a bit more awkward.
Handedness in all cultures is related to codes of chivalry, and western and eastern clothes (flys for pants, buttoning on shirts, flaps on Keikogi or kimono, robes or kilts) are generally right-handed for cross-body weapon wielding in men's clothing.
Women do not typically wield weapons cross-body and so do not need to worry about their lapels, flaps or flys catching on their weapon guards. It is also a sign of their "weaker sex" and need of protection that their clothing is "left-handed." Thanks, Tailors!!
Mores about right-hand dominance vs left-handedness can influence dress codes in specific cultures, especially in Middle Eastern and Indonesian dress codes.
Modern tailoring and dressing is individualized and can deviate from traditional and cultural dress codes.