Please note the discussion part. This is not a place for ideas to be shredded apart, but for modifying and improving.

Now lets get started with the list. Feel free to add suggestions and discuss points made.

1. Heavy is in need of some buff
His natural enemies are the Sniper and Spy. However, he now also has soft-hard counters from the Scout, Soldier and Demoman.
A suggested buff is to increase his firepower at mid range to become a threat to the other 3 whilst leaving his natural counters safe. This would help by making Scouts think twice about attacking the Heavy then retreating to mid range where he can barely be hurt, the Soldiers and Demomen would then also have to consider whether to attack the Heavy or not as generally they stay at mid range and blow the Heavy away whilst taking minimum damage. It would suit the role of a Heavy as it would fulfil his title as the BEST Medic buddy, which he currently isn't.
Another fix suggested is the minigun's windup time. It should be able to spin back up quicker if you had just spun down, which you currently cannot. This would help when classes like Scout wait for the spin down and know they can run in and attack the Heavy who is then completely defenseless for a second.
Another buff is immunity from knockback. The Heavy is supposed to be a big guy with 150kg of gun in his hands, but can still be tossed around as much as a Scout who is a thin arrogant little baby. If not immunity, increased resistance to knockback, although it has been suggested that immunity to all knockback be available when the Heavy is crouched and spun up. This would help the Heavy against all his not-supposed-to-be-hard&soft-counters since they all knock the Heavy into orbit. The Scout can utilise corners to run in, knock Heavy back, run behind corner reload, repeat too fast for Heavy to get a shot in on him, but if the Heavy is more resistant, the Scout would retreat as he should and attack from another angle or wait until the Heavy is busy with something else.
That is all for Heavy.

2. Engineer needs a desperate buff
The sentries are good against new players but are too easily defeated by those who have played more than 5 minutes. They are too binary in a sense.
A suggested fix is making the sentry instantly lock-on to anything in its range as defined by the blue zone. So anything that steps in the blue zone originally seen by the Engineer gets shot immediately upon detection. This would help the Sentries become more powerful and useful and prevent those cornering Soldiers, Demomen and Scouts. It really would fulfil the role of AREA DENIAL (ie you come in, you get shot immediately). It denies access to areas to everything except Spies who can still be the counter to this.

3. The Medic needs his weapons balanced
An old issue that never got fixed. The Blutsauger is a complete upgrade to the Syringe Gun which has suffered completely now that the crit system has gotten even rarer (and crits do come out for the Blutsauger as well). The Ubersaw is too good for the Bonesaw as even with the slow speed, the 25% uber is good enough for the Medic to never have to use the Bonesaw. Combined with the highest crit ratio, the Ubersaw is just like the Bonesaw with the feature of 25% Uber added.
For the guns, there are loads of suggestions. Giving uber per syringe hit. Removing the passive regeneration whilst carrying the Blutsauger. Increasing the crit ratio of the Syringe Gun. Putting the power of the Blutsauger to 3 hp per hit at any range. Increasing the range and speed of needles from the Syringe Gun. Pick your favourite, there are loads.
For the saws, there aren't as many. Giving 25hp to the Medic per hit would be good but you could call it overpowered in a melee fight. Increasing the uber meter or making it last longer would make it more viable against the ubersaw as you may not be able to charge up as fast but they would last longer and reward your patience. Another option is allowing the ubermeter to deplete at a constant rate and allow dual ubers (something which was difficult and yet was still nerfed). Again, take your pick.

If you have any suggestions, here is the place to put them. Discuss these in a friendly way please gentlemen. No flaming or tearing them apart. Suggest improvements only upon ideas rather than simply saying it is a stupid idea.

The heavy I think should have more health rather than his gun tweaked, but that's just me, I don't play heavy that much.

The medics weapons, I found that the bonesaw's higher hit rate is noticeable, but there's no real point unless you want to play as an assault medic. And medic is not my main class anyway.

As for the blutsauger, it is as you say a complete upgrade to the normal one. The only thing that makes the normal one worth having is if you heal a lot (as that makes critical hits more likely).

Heavy is fine. A good heavy in a decent team will be incredibly powerful.

Having a sentry lock onto anything within its range without being able to see it is both incredibly overpowered (far less things can take it out) and broken (lock onto targets it can't see and targets it can see then confuse it).

No comment on medic weapons, they are widely regarded as too strong.

The sentry idea is just farcical, imagine that if you wait half a second before you pop the uber after coming round the corner and your heavy has been pushed back behind you or worse DEAD and you're just sitting there dicking around with no one to uber.

The Medic goes first. The Heavy goes around, gets attacked by the sentry, the Medic goes ahead to draw the fire, the Heavy pushes up to close range, the Heavy destroys the sentry. And there's more than enough uber to do that. If the Heavy gets killed, the Medic can be blamed for not timing his uber correctly.

Whilst an interesting point, not everyone is going to play like that. I usually see medics hanging back a bit when they have ubered someone else.

The point though was that no matter who went first, if the medic ubered too late, then either he or the heavy would die because the sentry would know they were there.