Sorry. Completely forgot to reply to this. haha
So Mewtwo is a very gimmicky character that depends heavily on the other player not knowing his gimmicks.
How Roys beat Mewtwo is by learning two of his gimmicks.
A.) His teleport.
B.) His combo-breaker(s).
First off, you have his teleport. This may not seem like as much of a powerful tool when compared to 3.02, but let's take a closer look...
His teleport can be used to obtain a perfect sweet spot when absolutely parallel to the ledge. His teleport autocancels when landing from the air. His teleport gives him a decent approach (which can make a decent crossup if he knows his spacing). His teleport also allows him to steal the ledge from Roy during the hang-time of his up-B. And a smart Mewtwo will take advantage of all these different qualities to combat a Roy.
I will start with the first quality. This is a simple fix. Just grab the ledge and force him onto the stage and if you can catch him before his autocancel landing, you can obtain a free punish. Your go-to punish would probably be a ledgedash --> grab --> dthrow --> flareblade. As a Mewtwo, it is really difficult to avoid this punish unless he gets a perfect autocancel teleport to roll away.
The teleport's second quality is a little bit harder to deal with due to the mechanics of an autocancel. If done correctly, it should be (nearly) impossible to punish him. However, most Mewtwo's aim for the autocancel from the ledge. Now that you know this piece of knowledge, you can stand a few feet from the ledge in what I like to call the "sweet spot" when fighting the Mewtwo. Why do I call this the sweet spot? Well it's simple. This is the spot where you can punish literally anything the Mewtwo does. If he decides to autocancel, watch for his ledge release, then do a pivot grab to catch him out of his teleport or, if he doesn't do it perfectly, you can even get an fsmash. If he decides to roll, you can either go for a regrab into dthrow flareblade or just fsmash him. If he decides to neutral getup, just ftilt him . If he goes for the jump, just jump up and flareblade him. And due to your spacing, you shouldn't have to worry about a getup attack. This position is where you'll make most of your profit. You want him to be in this position so that you can get maximum option coverage.
The third quality is something you have to feel out for yourself. All Mewtwos prefer to tele-approach at different times. Just play out the neutral until you get a good read on when he wants to tele-approach, then you have your choices from there. If he goes for maximum-range tele-approaches, just wait for his cue that gives his approach away (most players have a cue) and wavedash back fsmash. If he goes for the crossup tele, just shield it --> wavedash OoS --> grab --> profit.
The fourth and final quality is oddly under-utilized in the Roy MU. I have no idea why, but I have only met one Mewtwo who has done that against me. This is the hardest of the teleport qualities to deal with. No matter what, if the Mewtwo knows this, you WILL have to land on stage and the Mewtwo WILL (most likely) confirm a punish. Most Mewtwos will do a neutral getup --> grab --> bthrow to reset the situation. In this situation, you want to do an up-B that will land you as close to the ledge as possible. This will force the Mewtwo to do a pivot grab out of neutral getup. If you're lucky, this will mess him up, and if you're even luckier, you will edge cancel the up-B and get sweet, sweet vengeance with an early up-B for 15-20% on the Mewtwo.
Second off, you need to learn how to deal with his combo-breaker(s).
The reason why I have a parenthesized 's' is because his fair isn't a true combo-breaker unless you're really messing up your timing. This is such an insanely simple fix. Know. Your. Timings. If you know that he's about to come out of hitstun and you're near him, 10-to-1 he's going to either do a nair or fair. Now that you know this, you can opt to drop the combo early to bait out the combo-breaker for an even longer combo or you can obtain a hard punish with an fsmash. If he's too high to fsmash, scare him with an empty jump --> fast fall to bait the breaker --> uair or do whatever aerial you want depending on the situation. Once he does his combo-breaker, he will be susceptible to a large variety of punishes, which are all ugly because Roy has a great combo game as well as both an aerial and grounded kill move. Small edit: You can tell a Mewtwo wants the combo-breaker when he DI's in. If he's DI'ing in, you can shield the breaker and confirm a grab or you can just fsmash him for DI'ing in which will kill him at earlier percents because, well, he's DI'ing in.
Now I guess I should take some time to answer your questions after all that rambling.
When it comes to Mewtwo's weight, he is actually amazing for early-percent combos. Your fthrow, if DI'd incorrectly, can lead to either a regrab, fair, or nair. Your dtilt leads to some decent uairs and if you pressure him hard enough in the air, you can force a teleport. If he tries to DI your uair down for a combo-breaker, just L-cancel it and do an utilt. both fairs and uairs are pretty good tools for comboing Mewtwo. Essentially, he's just a whole difference combo-weight to learn for you. Anyone can be an awkward combo-weight if you don't get enough MU experience against them. I used to believe Luigi was hard to combo until I learned to bait out his nair. Now it's pretty easy for me to combo him.
Also, what moves of his do you think can contest Roy's spacing? His bair is the only move I've had any difficulty with and that is truly easy to beat once you learn the timing of it. If you learn to wait-out the bair, you can actually do a shorthop --> instant fair for the punish which could lead into a small combo string. If you clarify further on this subject then I may be able to help you.
Nair should never be a problem for Roy unless the Roy is misspacing his approaches. litterally almost everything you do out-spaces Mewtwo's nair. But if the Mewtwo is really keen on doing defensive nairs, just do a short hop, into a fast-falled empty land just outside of his threat-zone and fsmash him. The short hop should trick him into thinking you're going for a reckless approach and the quick land fsmash should catch him on his punish attempt. If he knows this trick, then go for a tomahawk. If he knows about the tomahawk, he will either go for a spot dodge or roll. wait out the spot dodge and fsmash or if he rolls just learn which way he prefers to roll and chase it next time. Otherwise, just be smart with your spacing and you shouldn't get nair'd.
If a Mewtwo is spamming shadowballs, practice your powershielding. No. I'm not joking. I have a Mewtwo friend who rarely SB's me anymore. He doesn't like the fact that I have an 80% success rate on his SB's. SB is so easy to powershield once you get used to it. If you can't seem to pull this off though, treat his SB's like Sheik needles. Just shield one, wavedash forward, shield the next one, wavedash again, and keep doing this until you're near his threat zone. He should be scared to throw a SB at this point because he doesn't want to get punished. Most better players will try their hardest to be constantly within this threat zone to avoid SB spam.
If you have any further questions, feel free to ask. I used to play a Mewtwo constantly and he hates that MU now. haha
Sorry if there are any grammar or spelling issues. It's a little late here and I don't feel like dealing with the corrections.
EDIT: I guess you can't really consider B. a gimmick, but meh. I like to consider combo-breakers gimmicky because I'm a scumbag that relies on combos. =P