You are a Monstrosity

Your size is Medium.

Since the experimentation on your body has left you as part spider you have both a walking speed and climbing speed.  Your walking speed is  40 ft. your climbing speed is 40ft.

If you move at least 30 feet straight toward a target and then hit it with a melee weapon attack on the same turn, you can immediately follow that attack with a bonus action, making one attack against the target with your fangs

You count as one size larger when determining your carrying capacity and the weight you can push or drag.

In addition, any climb that requires hands and feet is especially easy for you because of your arachnid legs. When you make such a climb, you are not affected by webs and can climb on slick surfaces and the ceiling.

You have fangs that you can use to make unarmed strikes. When you hit with them, the strike deals 1d6 + your strength modifier piercing damage, instead of the bludgeoning damage normal for an unarmed strike.  The creature hit with this attack must make a Con saving throw DC 15 or take an additional 1d6 poison damage 

Your monstrous connection to spiders gives you an intuitive connection to their world and the animals within it. You therefore have proficiency in the following skill: Stealth.

You are descended from drow, therefore you gain both of the following traits:

Fey Ancestry

You have advantage on saving throws against being charmed, and magic can’t put you to sleep.

Sunlight Sensitivity

You have disadvantage on attack rolls and on Wisdom (Perception) checks that rely on sight when you, the target of your attack, or whatever you are trying to perceive is in direct sunlight.

Due to your drow ancestry, you gain proficiency with rapiers, shortswords, and hand crossbows.

You are half spider. you gain superior darkvision and websense as long as you are not in direct sunlight.  

Your darkvision has a radius of 120 feet.

You have websense (can tell the exact location of anything that is in contact with a web you are touching)

due to the monstrous nature of your being, you have disadvantage on all charisma checks. 

You have a hard exoskeleton over your spider half.  Your exoskeleton provides you a base AC of 11+ Dex. You can wear light, medium, or heavy armor, but the price for custom armor to fit your body is 2-3 times the price and materials cost of standard armor (Determined by DM).