ok two questions I have about ROB.
1. what playstyle would he be identified as?
2. what are some characters/playstyles that can handle his weaknesses.
The optimum playstyle (based solely off his moveset and physical characteristics) is a zoner that has a pretty solid Follow-Up/Agressive Punish game once he confirms off a set-up. He is a character that transitions from a turtle-ish state to a decently aggressive one better than most of the cast - usually off a grab, N-air, or gyro trap. At low percents, the opponent can eat a quick 50-60% with the proper set-up and subsequent reads.
His flaws are that he lacks a solid "get off me move" like many of the cast (Mario/Luigi come to mind with their neutral airs, as does Sheik with a lot of her kit, among others). This acts like a multiplier to the combination of his weight, aerial speed, and fallspeed. The two together result in him having a really tough time getting down. Also, he has a pretty predictable and non-versatile recovery. As a result, if most of the cast touches him from 0-15%... you might as well surrender the 60%+ that's gonna get tacked on unless the opponent goofs. I personally play every stock when at 0 as if I've already taken the 70%... bc if I get touched, that's what's gonna happen. He struggles against quick/nimble characters that can traverse/navigate his zoning game, and those that have a fast CQC game & set-ups/confirms off of it. Also, the fact he has a terrible blindspot at about 45 degrees in front of him, and for the bulk of the area behind/below him certainly doesn't help.
EDIT: I also would say he has a bit of trouble safely killing (in terms of moves that are safe to use, and percentages that ROB is at to be able to safely use the move) since the U-throw nerf. He has a few U-smash set-ups (usually off techreads and gyro drops) or OoS... but I find that its a super hard, risky commitment (as are most of his kill moves). D-throw U-air stops being a combo generally before kill percents (unless ROB is at a low percentage) and is too reliant off reads/baits to be considered a true set-up, imo.
I'd say ROB is a more zoning based character with his projectiles and neutral air, but can definitely go aggressive when he needs to.
I think his biggest weakness is his size. So characters that are able to get in on ROB and combo him generally win the MU.
Characters like ZSS, Mario, Fox, Sheik and Pika all do pretty well vs ROB. At the same time though, I've noticed Pikas and Sheiks have a hard time closing stocks, and with rage and the fact that those two characters are really light, the percent lead doesn't mean as much as it might in other MUs
Also, Villager is a pain in the *** to fight since he can pocket ROB's gyro, and as long as he pulls it out once every 30 seconds (or w/e.) and re-pockets it, ROB could have to play the majority of the match without having access to his gyro
These are all tough MUs for ROB, for sure. Can't say much about Pika as I haven't faced a competent one, but on paper it seems he can set up kill options through thunderjolts as well as QA (in addition to reads, and I believe a few frame traps, esp. with heavy skull bash).
Sheik really doesn't have a hard time killing ROB... or, she shouldn't. He poses no CQC threat to wall her out outside of jab, but I think hers comes out quicker (and I believe her F-tilt comes out just as quick & offers comparable range) + she can act after shielding ROBs jabs/d-tilt before ROB can do much about it. Sheik really can just "press buttons" on reaction to most of ROBs kit. Also, Sheik can BF over a grounded gyro shot, and I believe as laser depending on the range and if he (or she) uses a jump. ROBs up+B is target practice for bouncing fish and Vanish & his aforementioned physical characteristics allow Sheik to set up for U-smash kills more easily. Plus, if she spaces correctly... f-air is safe on shield and she can bait an action from us (ANY action) and punish fairly hard.
The Villager MU is annoying as heck. Learn to rely on laser once the gyro is pocketed, as that's where the bulk of your safe damage will come in (esp. when Villager uses lloid from a far distance) and know/understand the timing needed to punish moves (such as lloid). Dont fux w/ F-smash, as that thing has ridiculously low cooldown and is super versatile for the strength it has. Also, F-air is probably ROBs best aerial in terms of chip damage utility, as N-air is too slow compared to slingshot to be able to use it successfully (and often) at its typical effective range. I know the latest patch nerfed his recovery... so that helps us a bit in this MU, and I think something was done to his F-smash as well (not 100% sure on that one).