The weeding out usually has a few stages and is usually self selecting:
-Plebe summer/year: A lot of guys show up thinking they know what fitness is, or being the baddest kid from their suburb. Consequently, they weed themselves out by realizing they either can't, or don't want to put the effort into, getting into the kind of shape necessary.* This is especially true with the swimming side of fitness.
Another separation around this time is guys who say they want to be SEALs just because its the hardest and most bad ass thing you can do from here, but don't really understand the mission or what makes SEALs different.
2/C Year: After PROTAMID, some guys decide they really want to be Marines/Fly/whatever, and so stop trying for SEALs. This is also when the screener happens. Usually like ~70-100 people sign up for the screener during a given year. Some people get intimidated before the screener even starts and drop, and then more drop during the screener. Those who complete it get ranked and the top ~50 or so get a SEAL cruise. It is virtually impossible to get SEALs without a SEAL cruise.
1/C Year: Mids get ranked on SEAL cruises. There's a mini-Hell Week, among other things, and so some guys decide that SEALs isn't for them. Probably around 40-50 (depending) put SEALs first at service selection. There's a very rigorous interview process; those guys get grilled. After the interviews, during which a bunch of SEAL officers and senior enlisted are brought in, they make the decision and the lucky few make the cut. 28 from my class are going SEALs, another 16 are going EOD, for which there is a really similar but separate process.
It seems, from looking at the list of guys from my class who got SEALs/EOD, GPA wasn't a huge factor. There's some academic rockstars in there, but there's also guys who I'm pretty sure are sub 3.0. The biggest things are physical and military performance.
Military performance is stuff like aptitude rankings, leadership positions, conduct offenses, etc. Honor offense=pretty much automatic no go for SEALs/EOD (or Marines, for that matter), and the same goes for some major conduct offenses. It seems (looking from the outside in, obviously) that there's not really any hard and fast rules here: if you, say, messed up and got a major conduct offense, you could still be in the running, but you better have stellar rankings and recommendations otherwise and destroy the PST. Similarly, if you beast the PST and have a 4.0 it might not matter if everyone in your company hates you and you've never had a leadership position.
The only official program that exists to prep mids for SEALs is VAST, which is exclusively for varsity athletes. While that may seem weird, it exists to give those guys the skills and fitness that they might not get otherwise. For example, a guy on the lacrosse team isn't otherwise going to find time to hit the pool, whereas an intramural warrior has piles of time to do so in addition to other workouts. There's always a SEAL officer on the Yard (right now I think there's two, but one is actually a JAG teaching in the law department), and sometimes they will lead workouts in the mornings that are open to all. Showing up at those workouts is a good idea, especially for plebes and youngsters who want to get a feel for where they need to be and start to get visible with the officers who might be choosing the SEAL selects.
Another, new, thing is the Special Operations Team but I'm not 100% sure what they do.
Some guys try out for the Combat Arms Team, which does lots of combat fitness type workouts and is seen as a good prep for Marines or SEALs. They have an intense vetting process though and you can only try out plebe year, so not getting in does not mean you can't get SEALs.
*For perspective, this is sort of off the top of my head but the PST scores you'd want are:
Run: sub 8:15
Push ups: 110+ (good ones)
Pull-ups: 20-25+
Sit-ups: 110+
Swim: sub 8:00