Is it weird to tell your partner you love touching them

If it is a friend, then yeah, probably. But since you said "parter", then no. Absolutely not weird at all.

I would love to be able to say those words to someone.

I love feeling my girlfriend's touch. Hugs, cuddles, or when we hold hands outside. Even if I have a lot on my mind, when we snuggle together on the couch in the evening to watch a movie and she rests her head on my shoulder, I feel her silky hair against my face, or has her hand on me, I somehow feel a little bit better.

Not that big a deal

Obviously normal and most would prefer you do even, usually even asexuals (provided you just meant like cuddling).

If you walk up to a stranger, put your hand on their shoulder, and say, "I loveeee touching you," that's also normal. Just kidding. That's weird.

Eh

As long as they've said yes then you can but if they have said no then do not touch them at all.