As for KO setups, I dumped a big list of the ones I use:
That actually reminds me that I created a little cheat sheet for MK's combos a while back but never posted it. Granted, most are not true combos due to DI but they works for most of the cast if you add or subtract percent based on character weight (Sheik was the test dummy here):
0% Combos:
D-Throw > SH N-Air 17%
D-Throw > Dash Attack > Up-Smash 17-22% (Character specific)
D-Throw > Mach Tornado (Character specific)
Dash Attack > Up-Smash 15%
Dash Attack > SH Nado? 26% (Character specific)
0% to 90+% (AKA Bread & Butter AKA MK's Diddy Kong D-Throw>Up-Air)
F-Throw > Aerial Shuttle Loop 21% (KOs at later %s)
*F-Throw comes out on frame 4 after a grab so, unlike D-Throw, DIing the throw is very unlikely!*
**F-Throw while it has less knockback (good for combos) and more damage, it has less hitstun than D-Throw. So make those inputs quick**
35~% (KO Percent)
F-Throw > FH Up-Air > Jump Up-Air > Jump Up-Air > Aerial Shuttle Loop 36%
Down-Throw > FH Up-Air > Jump Up-Air > Jump Up-Air > Aerial Shuttle Loop 34%
F-Throw > FH Up-Air > Jump Up-Air > Jump Up-Air > Air Dodge > Mach Tornado 44+%
Down-Throw > FH Up-Air > Jump Up-Air > Jump Up-Air > Wait > Air Dodge > Mach Tornado 42+%
Down-Throw > FH Up-Air > Jump Up-Air > Jump Up-Air > Jump Up-Air > Aerial Shuttle Loop (KO Combo)
Up-Tilt > FH Up-Air > Jump Up-Air > Jump Up-Air > Jump Up-Air > Aerial Shuttle Loop (KO Combo)
Up-Tilt > FH Up-Air > Jump Up-Air > Jump Up-Air > Aerial Shuttle Loop 32%
40~%
F-Throw > SH Mach Tornado 28~%
50~%
SH D-Air > Mach Tornado 26~%
84~% (KO Percent)
Dash Attack > FH Shuttle Loop (KO Combo)
90~% (KO Percent)
F-Throw > Incorrect/No DI > FH Shuttle Loop (KO Combo)
Up-Tilt > Incorrect/No DI > FH Shuttle Loop (KO Combo)
101% to 130% (KO Percent)
D-Tilt > Missed Tech > Dimensional Cape Slash (KO Combo)
D-Tilt > Grounded Up-B (KO Combo)
D-Tilt > Tech-in-place > Mach Tornado
Single Move KO% (Off-top, no Rage required):
Grounded Shuttle Loop KO Percent: 98%
Forward Dimensional Cape Slash KO Percent: 107%
Up-Smash: 108%
Up-Throw KO Percent: 156%
Red = A likely opponent input
Obviously anything with red isn't a real combo but I listed them because, unless the opponent is experienced with MK, they're very likely to make the input or lack-thereof required to make the combo happen.
I'll go more in-depth on all of those combos in a guide I'm writing soon.
Again, add percent to those combos based on weight (try them in training mode) and they work on most of the cast. You do have to keep rage in mind tho as some combos stop working with high rage but some also KO earlier.
As for just dealing with heavy characters and heavy-hitters overall, I bait attacks by playing aggressively and punish with F-Smash for a KO. I'm always just out of reach but applying enough pressure that big characters can't quite get their footing properly. And like Busken said, Bowser, D3, Ganon, and Bowser Jr. have exploitable recoveries and can be N-Air'd or F-Air'd out of their Up-B's pretty easily. The worst they could do is bat you back on-stage unless they recover low in which case they could stage spike you. Donkey Kong is a bit nastier since he can spike you with F-Air if he's coming from above but if he's forced to Up-B it's safe to chase after him. Mega Man's difficult but possible to gimp with a well-place N-Air but if you miss and he grabs the ledge, always use Dimensional Cape's intangibility to get back to ledge to avoid the Hard Knuckle punish.
I tend to get KOs from F-Smash and comboes off of throws or dash attack more than off-stage gimping them though. It's also good to remember that F-Smash has only 8 frames of ending lag so you can throw it out to bait reactions and punish accordingly.
I quickly threw together a video for you from a random FG replay that shows off spacing and punishing against Bowser. It's not the best but it's the only replay I have of a heavy character atm.