The lucky kids get help packing for their induction day, along with a good, accurate scale to squeeze out every gram of the weight allowance. Vernon is not one of those kids. He's on his own for last minute packing, and his scale is garbage that only does ballparks. In fact, Vernon's lucky that his dad bothered to try to protect him at all to get him to the age where he can go to the place where the odds of surviving to adulthood are one-in-four instead of one-in-twenty, and luckier besides that his dad even bothered to work for getting him into Scholomance at all. He does not get anything so thoughtful as 'help preparing.' He gets an extra stack of letters dumped on him as a surprise at 6 AM in the morning, an hour before he's to be yoinked off to school.
"What am I getting for delivering these?" wonders Vernon, who nonetheless takes them, nervously thumbing through the letters to see if he recognizes any recipients' names. Mostly: no. That'll be exciting. Hopefully they're in a language he knows. (English, French, Latin, and a smattering of Greek that's probably going to screw him over.)
His dad shrugs. Which is to say: Vernon is getting nothing but maybe some good will, but his dad's squeezing the last drop of usefulness out of his kid before he probably goes off to die. Great. But it'd be worse to have had someone else promise that he'd deliver them, and then not, and that's the sort of thing that'll leak in the four years until graduation, and anyway good will is nothing to sneeze at, so. He does last minute weight reallocation to make them fit.
Most of his weight allocation is only for himself in the sense that it is what's most likely to keep him alive. Which is to say: it is mostly for other people. Letters are the obvious and most light, and the healing powder to be mixed into a liquid is downright brilliant, but a lot of the things he's been asked to bring aren't necessarily smart, weight efficient things. He has a perfect list of everything he has, but it's divided more into who it's going to and what the weight to work around is before what's in each care package. Vernon sort of feels like he's not supposed to know, or judge. So he tries very hard not to. Even when the packet of gobstoppers is the stupidest thing he's ever heard of, and they clink around so obviously in his paper thin backpack that it screws with his situational awareness if he so much as twitches too fast, which will probably get him killed on the first day in, somehow. He would pack something around them, to quiet them, but that would dig into his extremely meager actual personal weight allowance, which is a pathetic 5.3 kilograms. Fortunately not counting the clothes he's wearing and the weight of the (light, thin) backpack itself, all so long decided in advance that their weight doesn't even really factor in anymore, but still.
He has one spare set of clothes, two extra sets of underwear and socks, a meager little unenchanted half plastic multitool that will probably break if sneezed on, a needle and thread, a (plastic) crochet hook, a tiny pair of scissors that can come apart, and as many glass beads as he could get that he has been sweet talking for years into being any good at holding mana, but still kind of leak a little. Other things work better, of course, but Vernon doesn't expect to ever get better, so he got started on the garbage mana storage methods early.
Vernon eyes the newly acquired letters, ditches the second spare set of boxers, weighs himself on his shitty inaccurate scale, and then starts doing difficult, irritating math problems in his head to squeeze just a little more mana into his set of (still leaking) beads to maybe pay the Scholomance the difference if he turns out to be estimating wrong. He's been generous with his margin of error instead of arrogant about what dehydration and no food for the last twenty four hours will get you, but he can't afford to lose any stuff that isn't his. Statistically speaking that is what is most likely to go, from weight distribution. He left his eyebrows alone when he was shaving himself, on the prospect that it'd make him slightly more personable, on this important first day, but maybe that's pointless and he shouldn't care...
He ends up not ducking into the bathroom with a razor, on the principle that he should trust himself instead of practicing self sabotage with too much second guessing. Also, he might lose track of the time, which would be the worst.
There is no one to see him off, when he goes. His dad's already left, muttering something about finally being able to get a good night's sleep. It shouldn't hurt, but it does anyway.
And then he's gone.