Yoshi's double jump is similar to super armor in every way, except that if super armor is in fact not possible to be broken, he doesn't share that similarity. That still doesn't account for the fact that some of these super armors listed can be broken by many powerful attacks.
If Yoshi's double jump is only a weight change what accounts for the fact that he is knocked out by certain attacks and not others? Surely it's a variable determined by either damage, knockback, or stun time of the attack, which would all be held true for what can break Kirby's down+B, grabs, etc...

You played Yoshi some in Melee, right?
I mean, forgive the straightforwardness of this post, but you kinda summed it up here.
"Yoshi's double jump is similar to super armor in every way, except that if super armor is in fact not possible to be broken, he doesn't share that similarity."
That seems to make everything clear, but just in case it isn't, I'll go a bit further by touching on your second statement. The reason why Yoshi is knocked out of certain attacks and not others is EXACTLY because of the reasons you stated (except it's a combination of [and], not a choice between [or]). Damage (or, more accurately, power) dictates mostly when the jump is broken. Knockback (as shown by Falco's shine, Roy's Up+B, and others) can break the jump at vastly different percentages due to the unique (and often static) properties of the attack. Stun doesn't play such a huge role, but can mostly be bunched together with knockback as it's quite late and I have no examples that I can really bring to mind.
But yeah, all this stuff has been in Yoshi's jump since 64 except for the fact that it's been getting broken earlier and more often in each iterated--especially in this final--version of Smash. That's about it. I guess you should PM me if you disagree because I won't be checking this thread that much. I just wandered in here earlier and saw your post, hahaha.