Is there a general name for this: "The more you X the more you'll Y"
Some more examples:
"The more you want the more you need."
"The sooner you mow the lawn the sooner you'll be able to relax."
Maybe there's not a name for this specifically, but is there a name for expressions like these that have some blanks that get filled in.
Also, to me it sounds more awkwarder when the adverbs are different such as
- "The more you want the less you have"
Is that just me or am I breaking a rule?
I don't think there's a particular name for that snowclone, but maybe you'll be satisfied in knowing that that general type of phrase is called a snowclone.
They've also been called "catch structures", but snowclone is becoming much more popular, no doubt in part at least because it's a much more amusing name.
Is that just me or am I breaking a rule?
Yes, but you're keeping to the pattern to an extent too. This is common enough with snowclones. Consider the snowclone "X is the new black". This started with announcements about colours being the "default" "go-to" colour the way black has been since Coco Chanel and Jean Patou in the 1920s. (Actually it started with "pink is the new black" referring to the popularity of pink in India and black in New York in the 1960s, but later it was about new temporarily predominant colours).
Following the pattern "[colour] is the new black" (the phrase seemed to really take off in the British Isles only when brown was the new black for a while in the 1990s) there later arose "[colour] is the new [colour]" (I think blue was the new brown after that, but I'm not sure), "[thing] is the new black" (after the film of Brokeback Mountain apparently "gay is the new black", though this had a much greater effect on straight people in the movie business than anyone else) and "[thing] is the new [other thing]".
Clearly each of these are wider or narrower forms of the same basic snowclone, differing in just how far from the original template they vary, but still recognisable as fitting it. The better-known the snowclone, the looser it can be, because that familiarity means that you can go further from the narrower template while still producing a recognisable example of it.
They are called snowclones, a term coined by some of the linguists over at Language Log. A more technical term might be phrasal template.