While the above contributor is right that weight itself doesn't affect damage, a cursed flying scroll will still increase a weapon's weight and damage. Since snails have so few equipment slots anyway (Back, Shoot, Ammo), it's almost impossible to get past Light equipment weight. It's not a bad idea to use cursed flying scrolls on your primary thrown weapon, once you have a good one.
Since going past Light equipment weight is so difficult for a Snail, consider spellcasting! Snails are just as capable with magic as anyone else, aside from their mana being slightly weaker than a Yerles or Goblin. Still better than a Golem.
Of thrown weapons, your best bets are grenades and shuriken. Sound damage from grenades can incapacitate several enemies at once, and the bleeding effect from shuriken adds a lot of extra damage (as a snail, you have low speed, and bleeding inflicts damage for every one of their turns, not yours. It's the same principle that explains why shuriken and poisons are so deadly against Quicklings and Bells). Consider swapping between a grenade and a shuriken as the situation warrants, at least until enemies start developing Sound resistance.
Since Ammo-slot items provide stat bonuses too, you can even use more traditional ranged weapons, like bows, crossbows, guns and laser guns, if you can find appropriate ammo for them that provides either stats you need, resistances, useful enchantments, or all-important speed bonuses (spirit cloth bullets? Yes please.) IMO, guns are the better choice for taking advantage of the ammo slot - the bulk of a gun's damage comes from the gun itself, and not what it's loaded with. You can more easily sacrifice some ammo damage in order to get good enchants and bonuses from an otherwise-bad material type.
The ability to ride is a godsend. Get the little girl pet (naturally) and ride her everywhere. Move up to a Yowyn Horse when you get the money, and relegate your girl to melee duty until you can get something more formidable. If you can somehow get 3 blue capsule drags before month 12 rolls around, go get the Kaneda bike. If not, there's always next year, if you survive that long. The cub, if you can find it, is a good intermediary between the Yowyn Horse and Kaneda Bike. In addition, it has ranged AI by default and will shoot enemies if provided with a ranged weapon - it's one of the few (if not the only) 'comfortable' rides that has this feature.
Using SHIFT+T to throw potions is an often-underestimated way to contribute to a fight, and snails are just as capable potion-throwers as anyone else. Poisons and dyes both cause poison damage (and again, damage-over-time effects are useful for you for reasons I explained above), and hitting foes with potions like Blindness, Paralysis, Confusion, Sleeping Drugs, Slow, Weakness, and Weaken Resistance can significantly soften up tough enemies to let your pets tear through them, and they're pretty common finds. You don't even have to worry about throwing cursed ones. Cursed negative potions are even better in some cases (such as throwing cursed sulfuric acid - it does more damage than uncursed or blessed acid.) Heck, even booze is can be useful (being drunk reduces an enemy's hit rate) All thrown potions do a little bit of damage when they hit, too (glass shards are a pain.)
Finding negative potions to pitch at enemies shouldn't be too hard. Magic shops typically carry them, and they're fairly common in all dungeons (including the puppy cave) at all difficulty levels. Dungeon diving is probably the last thing you want to be doing as a snail, unless you're very, very well prepared!
As for what deity to worship, Lulwy is an obvious choice - she provides speed, and you're just about the slowest thing to ever exist that isn't wholly immobile. The Black Angel is still the arguable-best of the Servant pets, and the Wind Bow is an excellent pet weapon, and you can use Lulwy's Trick and the Gem Stone of God Speed to further enhance your abysmal speed in emergencies. Opatos or Jure might be worthwhile too - but if I chose either of those I'd probably go apostate for Lulwy after getting all three god gifts and then find somewhere safe to hide while the Punishment wears off.
Consider special action feats. Touch of Hypnosis can pretty much incapacitate an enemy from melee range, allowing you to inch away from them in relative safety. Remember to use * targetting to try to order your pets to focus on something else. You don't want them to wake sleeping ugly up until his buddies are disposed of. Touch of Poison has all the benefits of poison in a permanently-available touch attack. Fire Breath destroys loot and can both hurt and tick off allies, but in Elona+ Control Magic will alleviate the problem a bit if you can get it. If you gotta choose between losing out on loot and frying a room to survive, fry the room.
If you play Elona+, it adds tons of skill-related special actions, many of which would be useful to a snail. I'd imagine that Shining Wave, Attribute, and BakuretuKen would all be useful for a snail in the long-run (especially since Martial Arts is your only melee skill).
Rods of teleportation (and rods in general, actually) are even more valuable for you than they are for anyone else. You need to get someone out of your face for a while? Zap them with one of these. Or if your pets are leashed and you're surrounded, zap yourself. Other creatures are faster than you - you probably can't escape them without a head-start, and a rod of teleportation is exactly the kind of head-start you need. It's the tool of last-resort - if all else fails and you're going to die next turn, going poof or making your attacker go poof right before the deathblow comes can save your life.
Finally - watch out if you travel around Palmia, especially if you enter from the west. There are cleaner NPCs, and they like to salt snails when they see them. You get salted, you're probably dead. They're nonhostile to everyone else. Take them out from afar if you can - blindness and paralysis will stop them from throwing salt at you, and Dark Eye is pretty easy to cast, even at low casting skills.
Best of luck, and I hope these snail survival tips help out.