Do a fecal, even if they are UTD they can still have some.
Check with your vet for a schedule. It will depend on your area, worms, resistances, etc.
We worm with ivermectin every 8 weeks and double dose strongid 2x/year. Works for us. May not work for everyone. Some people just check fecals regularly and rarely need to worm.
The primary weight builder is forage, aka hay. My Arab who is becoming less of an easy keeper as he ages is currently getting 1 3/4 qt basic grain and 2 flakes 2x/day plus what's left of the pasture all day. My taller and heavier MFT with health and now weight issues is getting 2 1/2 qts of his special grain and 3 flakes.
If it worked out to feed them more hay/forage we could feed less grain, but this is what works for us atm. So yes, the hay is for weight, feed them less hay and less overall they WILL lose weight. (Plus it's far more healthy to feed more hay less grain).
What brands do you have available at your local feed store?
Look up on here and check this out: Feeding Oats to Horses – The Whole Picture | The Feed Room
(skimmed it but seems informative)
Oats seem to be more of a thing of the past (yes they did used to be a big thing, so did lots of other things) and I won't ever use them. Since I haven't used them I don't know all the details but I'm sure someone else can explain it better but the main reasons outlined in that article are enough for me!
Definitely get rid of the sweet feed though. It's not nutritious or healthy.