To be strictly accurate, on a train, nobody has paid for a seat - you've paid to travel. A seat is a happy bonus. Which is how train companies can get away with squishing commuters in like sardines. I suppose if you're unable to stand safely you have a moral right to a seat, and train companies are trying to encourage it (& when I have to brave rush-hour trains from the last stop before the big London stations people are mostly pretty good about letting me sit down though I no longer "look disabled" [NJ tube had people LEAPING up for me as people by doors would tell them before I could ask myself]) but your ticket - despite the extortionate cost, isn't actually for a seat.
The huffing & puffing is a bit much I think - it's rude, basically. But on SE Fail, certainly, the 3-seaters (not 3-sweaters, thank you autocorrect) are not generous. They seat 3 Brownies in comfort & 4 can squish in without any overspill, but they've not much wiggle-room. And we're talking slender children here, too. If there are two "average" (for want of a better word) size adults on two of the seats, however, & they're joined by someone who is overweight, they just don't fit. Obviously how much they don't fit by is determined by the size of all involved & how they behave - space-encroaching is a thing at any size - but had another "average" person sat down, they would have all fitted, because you can fight off space-encroachers in a way you can't stop someone spilling over into your seat due to their weight. (I q frequently do battle with manspreaders on the tube: just because I'm small & a woman doesn't mean you can sit next to me practically doing the box splits with your elbows in my ribs. They invariably seem gobsmacked to find their limbs pushed back out of my space.)
It can feel very claustrophobic to be "squashed" in the window seat on trains full stop - if someone is encroaching on your space in that seat you really do feel trapped & unable to move even to read/use your phone etc. The person on the aisle seat can often feel rather close to the outside edge of their seat when there are 3 people sitting in the seats; when one of the 3 is overweight they will end up perching on the edge of the seat, as described by a PP.
As a PP has said, the OP is making sitting uncomfortable for others to the point they'd rather stand. Despite how precious seats are on trains. Other posters who are overweight have commented that they'd not squeeze themselves into a seat if it would cause other passengers discomfort - and given the frequency with which this is happening, either you commute with a chapter of Fat Shamers International, or you're causing people discomfort.
As to the "I don't take up my whole seat, how dare fat people steal what's left from me!" thing... as long as I'm left some breathing room, as it were, I don't, generally speaking, have a problem with this. I totally understand why overweight people will walk past other people sitting in the window seats of the two seats to sit next to me where there's more space for them. It makes sense, especially given the amount of shite overweight people have to put up with. Of course I get the odd person who apparently feels entitled to the entire double seat - but that happens with people who aren't overweight as well & I think is more to do with being an entitled arse &/or lack of proprioception than size! I've seen an overweight woman reduced to tears on a train because when she asked a man to move his McDonald's bag to let her sit down he bellowed that he wasn't "having a fat bitch" like her sitting next to him because "you'll crush me to death". As she stood there in shock he followed this up with "get away from me you fat cunt", then "is it my food you want fatty? Have it then!" and lobbing about a quarter of a burger at her that hit the side of her face & sort of a bit of her hair then fell onto her shoulder & down her front. A couple of guys from the other end of the carriage bodily ejected him from the train & some of us helped her clean herself up as best we could, but it really was horrendous. And all happened in one rush.
However, despite what arses like the bloke I mentioned above think, of course overweight people have the right to sit down on public transport, just like everyone else. But just like everyone else they need to be considerate of their fellow passengers, which in some cases may mean choosing not to sit in certain seats. And 2 people with suitcases shouldn't take up a 6-seater; and please don't block 2 of the 2-seaters with your pram and then take over the 6 & 4 seaters behind them with 2 parents, baby & 4 yo - and REALLY don't expect me to not only be Charmed And Delighted By said 4yo running up & down the carriage, but to entertain him when he demands it & I'm clearly occupied. Oh & if your child demands to play on a stranger's phone & they say no, don't try to wheedle them into it & then tell your child, loudly, as said stranger is alighting, that she wouldn't let him use it because she's "a mean girl whose mummy & daddy haven't taught her sharing". (I look quite a lot younger than I am & that one was a few years ago now.). Holding back on chuntering on about Teenage Mothers and What The World Is Coming To would also be good; especially, because actual teen mothers may be hurt by that sort of idiocy, if you won't find yourself looking a right twit because the "teen mum" & her sister start having a loud conversation about how it doesn't seem possible university graduation was so long ago etc. (My wee sister also looks younger than her age.) This is all without even getting into the eejits who drink on trains (or are just rowdy after doing so); or eat smelly food; or leave litter lying around; or smoke (especially weed, tbh, the smell of that makes me want to vom); or lech (or worse); or are otherwise anti-social feckers.