So i am nearly done with my part 61 ground school and I am getting ready to make an appointment with an AME. Problem is I am 5'7" and over 350lbs, even when I am in great shape i still weigh around 200lbs. I am 49, I do not have diabetes, blood pressure issues, sleep apnea and pulse is usually around 65. The question is - am i going to fail my medical because i'm fat? Will i even fit in the training aircraft when i do my discovery flight have wasted my time and money studying for my written?
You will have your neck measured for OSA. Due to the checklist they use, you will be deferred for an OSA sleep study, which you will not pass, and you will end up with an SI for a CPAP machine renewed yearly.
Then you will get a Basic Med medical and skip all of the rest of it.
That said... I was as heavy as you, although 6'2. My health warranty ran out at age 41, sugars and BP sneaking up and I could see the writing on the wall, so to speak. It's worth getting under control. Due to my anti-authority personality, I needed it to NOT be at the mercy of an AME's pen for me to actually deal with it head-on. Basic Med was the win for me there. You may take a different path.
$0.02. One of my old medicals just said "350+" in the weight box.
Just saw the second part of your Q. You will fit fine in a C172. You will be snug in a Piper cherokee/warrior/archer. If your instructor and your own shoulders are at the same position in the plane, one of you will need to move the seat fore/aft.
If you are training in a C172, be careful not to "hang weight" on anything. The door and the seat back are both vulnerable. There is a "dude of gravity" entry procedure which your instructor may not know. It goes thus:
1. Open door and attach it to the "catch"
2. Step right foot forward of the landing gear step. Place left foot on step if possible. Place your right foot all the way in to the right rudder pedal. You may need to put a hand on the seat BOTTOM or glareshield for balance until you get the moves down pat.
3. Launch yourself with left foot, with intent to secure one buttock into the seat.
4. Using your prehensile buttcheek, ratchet your head and torso into the cabin. Grab ABOVE the door frame, not the door itself. It is best that you do this with the right seat unoccupied. If your CFI got in before you, well, you two are gonna be real familiar with your head in his crotch.
5. Haul your left foot and leg in behind you while bracing your body using either the "A" pillar, or your seat BOTTOM. Never use the seat back for this.
6. Seatbelt. You can't get it on after closing the door.
7. Close the door. Party on.
If you get time in a Beech trainer (Musketeer/Sundowner) you will love the room. Same with a C182 Cessna if you have the means.
You should just rule out most things under 160hp now. You won't make useful load with an instructor on board, and if you do, performance will be marginal.