Cass is a Noxian, and if memory serves, all Noxians are required to serve no fewer than 6 years in the military, so idk about "no history of combat"

Millitary service does not always constitute combat. Her lore basically flat out states she was a spy who use her body to gain information via pillow talking.

"... Cassiopeia - despite lacking her sister's killer instincts - was equally renowned in at court for her stately character and elegance. Cunning as she was beautiful, the temptress could never be found far from the arm of any foreign dignitary, her wiles prying secrets from the lips of even the most wary attaché."

Not to say she isn't strong now, in her reflection she lifted up a bodyguard by the neck with one hand, that's pretty impressive. She also slaughtered a group of servants directly after her transformation.

I am tempted by amumu, since his weapons are tears and bandages. oh the great pain!

Nami perhaps. Similar to amumu, her weapon is water. In a 1v1 she would not fare very well against other champs

Evelynn. shes a top assassin in her lore but that doesn't mean shes really all that powerful she can kill lots of people but remember its not like shes fighting them toe to toe, shes stealthily killing them

What about Malzahar, his backstory is very empty Was a seer who lived alone by himself until he started walking west from his home for many months and got the powers he has now.

Udyr. He's got nothing to his name except for acting like an animal and getting Mystic Monk Training. He's got no magic and really just beats people senseless with his fists.

As far as weakest champion goes, it would be unfair to exclude a champion's connections. While karma may not win in a fight against Olaf, she also is de facto in charge of one of the stronger nations in the game. I would consider it inaccurate to consider her the weakest when she can snap her fingers and have 50 ninjas jump you from a bush.

Same thing for Heimerdinger. While he might not win in a tavern brawl, he has all the resources of the Yordle Academy of Science and Progress at his fingertips. He could probably build a laser to solve whatever problem he faces.

The weakest champions are going to be the ones that have no special powers and also have no friends. Miss Fortune has her guns... and that's it. She doesn't have a pirate crew, she doesn't have any substantial allies. She has a lot of money, but most champions have a lot of money.

I could say the same thing for Graves or Twitch. At least Ashe is a Queen and Caitlynn has Vi to back her up, but those others don't have anything to their name besides their gun/crossbow.