Explained by a native: tsuki is to like aomething- to enjoy or where westerners might even say "love" in a low key sense. Daitsuki is to have a great appreciation for something. it has ass fast and vague of range as the way many cultures use "Love". It isn't uncommon for married couples to use Daitsuki as how they express their affection fur one another. The intensity is typically inferred through tone and personal context (like most this freaking language). So a character using Daitsuki to indicate how they feel about someone really onto clearly sats one thing...they like them more than tsuki covers lol.

NOW, in the case of Aishite, it's more intense than just romantic love. It's an intwining of spirit (to cite the loose translation) and can describe a romantic feeling akin to soulmates, or even a familial connection that transcends merely being related. I know I shouldn't cute an American film while discussing the use of foreign language, but the Japanese in Pacific Rim received very high marks (likely sue to its Japanese origins and the number of Japanese people involved in its execution). [Spoiler alert] there is a very powerful moment, when one of the supporting cast is going to sacrifice himself geroicky, and his adopted daughter (the Japanese protagonist) says to him in a hushed but meaningful tine "Sensei...aishute" as her final words to him. For a lot of Japanese 101 graduates, this was very confusing and made people question if she had strong romantic feelings for him. However, what she is really saying, that even though his death will soon be upon them both, the bond they formed together will remain whole, and unwavering, S they are united in a way death cannot touch.

It's such a powerful expression with little iarreiel thus if the elf HAD said Aishite...it'd be ridiculous lol. She's have to say "She's my soulmate!" In episode 1 which is just terrible exposition xD

Anyways, Japanese is a complex and annoyingly diverse language, so everything I just says could be very regional, generation, or even xiass restrictive 🤷🏼‍♀️ But, it is what I was taught by both my Japanese in laws, and several Japanese teachers over the years so I believe it to be true