Green Hill Zone = DENIAL
We start off in the beautiful rolling hills of Green Hill Zone. From such a location you would never expect that it all begins with the mechanised invasion of Doctor Eggman, however despite how everything looks there is still spike traps and badniks. Despite the beauty of the place, it is not alright, there is still threat and bright sunny day with palm trees and pretty flowers would not change that.
Also, remember the Newtrons? Those badniks abilities were disguise themselves into the hill side in order to decieve. To not be ignored a spersay.
Marble Zone = ANGER
The first stage that introduce a natual threat. Lava! Often fire and heat is often compared to anger and there is lots of it. Marble Zone is also set in a series of ruins, ruins themselves could represent that things are "falling apart" as to say and beyond restoration. Another scene in mind is the scene where Sonic is chased by lava, this is in a sense a form of denial, refusing to face ones fury.
Also remember in Sonic 1 beta when Marble Zone had odd UFOs above it? Well while obselete in beta, they could also represent what is unknown and regarded as a threat above and beyond your calling.
Th Caterkiller could also represent "anger" in a sense that they are difficult to destroy correctly and if done wrong will scatter everywhere and cause plenty of damage.
Spring Yard Zone = BARGANING
Spring Yard is set in a city like place but also set up with parts simular to pinball. I believe the themes can be comparable to gambling but the city itself could also represent business. The whole stage could be about chances and business as well as slight construction theme which could represent that what is lost could be restored.
I suppose Rollers could be the badnik that represents Barganing given they move just like Sonic, yet hollow on the inside.
Labyrinth Zone = DESPAIR
The level is known not just for it's confusion but also the submerge areas. This level cna certainly be compared to "despair" as these hazards of the zone can be compared to the feelings we go through when in deep despair, such as the feeling of not knowing what to do or where to go all the more while being submerge in dread.
Star Light Zone = ACCEPTANCE
The zone is themed in city but mostly with a construction theme. Sonic accessend to reach the goal and thus climb up to enlightment. The name of the zone is about higher inlightment as well and the theme of construction being more major than Spring Yard could mean acceptance and restoration in ones life.
Bombs can represent Badniks of acceptance due to there suicidal nature. They have accepted death and go out with a bang.
Scrap Brain Zone and Final Zone
I believe that the game itself could be the "funeral" of Dr. Robotnik and that it is Sonic himself who is in grief from the loss.
The western backstory to Sonic 1 is that Sonic and Dr. Robotnik were once friends, but it was a lab accident that turned Robotnik into the evil Dr. Eggman. In a sense it was the end of "Dr. Robotnik" and a close friend of Sonic. Throughout the game Sonic pursue Dr. Eggman so in a sense Eggman himself could represent Sonic's personal "devil" in which he pursuit. He takes it on himself the responsability and has the power to do so.
My personal headcanon is that instead of Dr. Ovi Kintobor, it was Dr. Robotnik who was his good alias before Dr. Eggman (Or else how would he be related to Proffessor Gerald Robotnik?). I also like the idea that his "transformation" could be simular to the slow and pitiful change that Simon Petrikov went through than just "suddenly". I can imagine that perhaps there was more story behind Sonic's first game that was more accountable. But this is what we all like about the Classics is that we cna all relate to them somehow and all spin our theories around it.
Just a thought though. Might add more "Thought" blogs in the future.