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In my game I don't use the racial weapon rule as is, I count it as providing automatic proficiency only.

To make up for this I give each non-human race +2/-2 modifiers like 3.5 & COMBINE them with the subrace modifier provided.  So if you're a dwarf that gives you +2con/-2chr and if your subrace is hill dwarf you get a further +1con for a total of +3con/-2chr.  If you were a mountain dwarf you would end up with +2con/+1wis/-2chr.

It seems to work pretty well & highlights the differences between the races which I personally like.  I've been toying with the idea of eliminating the class-provided ability score modifier, but so far I'm still using it.  Yes, I realize this makes it possible for example a hill dwarf fighter to get +4 con(and no bonus to str, would this really happen?), but what the heck, dwarves are SUPPOSED to be really tough, and it gives them a real advantage to make up for not getting a bonus in str or dex.

I could not agree more with Kali-Mada.  I know that one of the main aims of D&D next is flattening the math/power progression & this is part of the reason for the demi-humans getting only +1 instead of a +2.  But your point about humans is entirely valid.  Why is every human fighter going to be a better fighter than a dwarf of the same class and level.  There are a few ways of handling this to make it fair to dwarves, elves, halflings (and half-orcs & gnomes when/if we see them).  Increase the demi-human bonus to +2 to a key stat and bring back a small penalty of -1 to another stat... for elves make the option CON or STR.  For dwarves WIS or CHA.  This could strike a balance: I know some folks think that the human stat bonuses are OK because the demi-humans get other, non ability score benefits.  While I understand this, I disagree.  The total bonuses that human characters get are +7.  That's too generous. 

Tim the Enchanter has some interesting ideas, though I have to say that I doubt that they'll allow any race get a +3 stat bonus at LV1.  But I also personally like the differences between the races and also would not mind a minor penalty to create some balance for the rules.

It's all good and pretty, and I agree that excessive Ability Modifiers may be bad...


But what does +1 or +4 from Strength matter when you are dealing 1d8+6d6+20 of damage already?
Martial Damage Dice and Martial Damage Bonus are game-breaker, imo.

(at least for raw damage, I haven't entirely tested the dice use for maneuvers yet)

They'd be the first thing I'd eliminate were I to play 5ed as it is right now.
Likely I'd substitute it for some house rules, probably bringing back multiple-attacks for high level characters. 

Game-breaking and broken in this case are slightly different concepts.

It's not "broken" because it works as a system on itself, but it does affect several other rules in a bad way, and that, to me, feels like "game-breaking" thinking of the game as a whole, interacting organism.

For instance, if you apply +6d6 and another +20 (or whatever huge ammount of damage of the sort, even if half of that much), your Ability Bonus to damage becomes utterly irrelevant, be it +0 or +4.
You already have an average +41 damage on each attack, so +1, +2 or +4 really matters not.

The same can be said for weapon choice. Things like "I'm focusing on one-handed damage so I'll choose a sword that deals 1d8 instead of a dagger that deals 1d4" become irrelevant... 1d4+41 or 1d8+41... no biggie.
In this system your level is basically all that matters to your damage output.

If you have multiple attacks, however, things change drastically.
Not only you have to score a hit with all attacks to deal the full damage, so your combat round will not be like: either no damage at all or huge ammounts of damage;
but also each small bonus you get here and there do count (a +3 from Str instead of +1, a d10 weapon instead of d6, etc), because those bits of extra damage will be applied for each attack individually and sum up.
Three or four attacks of 1d10+4 will deal considerably more damage than the same ammount of attacks dealing 1d6+1.

Like that, all the small choices you make along the way as you level count.

those are good points.  I guess I just think that damage depending on class and level way more than weapon and strength is a feature, and not broken.  Or at least something I'm willing to explore.  I feel like I would like to see weapon choice matter more . . .

And the justification for more damage is reduction in number of attacks.  You are right that the main flaw in this is that you either do a lot of damage or zero.  The main advantage is that it is faster and that you don't have cuisinarts of death as fighters.  A 3e fan could think of it is as every martial character automatically using power attack on every attack.  Then if you want to sacrifice damage for accuracy, you can do so through maneuvers which use your martial dice to do things like grant advantage to hit.  Martial dice aren't just damage, they are the instrument for using melee abilities. 

So the +6d6 damage represents a choice to not parry any damage, not attack multiple targets or not otherwise manuever in an interesting way.  the +20 damage makes as much sense to me as a +20 to hit applied on a decresing scale many times . . .