How to determine values?

Pacific Rim?

Are the robots going to be different? Or is each player going to have the same robot at the start?
Are the monsters going to be all different?
Can players have more then 1 robot?
Can a robot have more then 1 weapon?
Can a robot have more then 1 defence type?
Am I looking at a RPG, or a little war game?

The game is more fun if a robot has more then 1 weapon.
Since you have 2 arms and a torso (you could throw the 3 armed robot in :D)
Anyway, if each player starts with the same basic robot. There is more of a competition. And more the feel of fairness. You could even let the players choose different weapons.

I suppose you want to use dice to determine the hits? Or else it would be a simple calculating game.
I also suppose you want to have different monsters in each tier. Meaning I will be playing with the health and armor of those monsters too.
I will first suggest a simple tier for some weapons by simply increasing the damage. But keep in mind, you could also add specialism for each weapon. Like not upgrading the damage, but only the fire rate. But that makes things complicated and perhaps not needed.

Damage/hit is the damage,
Armor gets subtracted from this,
Then the real damage remains, <0 is 0
The fire rate is the number of dice you can throw for that weapon to determine if each dice is a hit or not. If you want, you can have different accuracy on that for each weapon.
Results for now:
What you get is that low damaging weapons do relatively a better job against low armor.

First some weapon suggestions, then an analyses on the effects. I also have this in a excel spreadsheet.

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Some suggested weapons with only damage and fire rate:
Gatling Gun:
Tier 0; damage/hit=150; fire rate=10
Tier 1; I don't know the number of tiers you want, but lets say each tier has 20% increase in damage. So 180 damage, then 210 damage, etc.
Tier 5; simply the double of damage.
Quad Canon:
Tier 0; damage/hit=240; fire rate=4
Light Laser:
Tier 0; damage/hit=90 + 100; fire rate=12 for each, a total of 24
Heavy Laser:
Tier 0; damage/hit=190 + 200; fire rate=3 for each, a total of 6
Rockets:
Tier 0; damage/hit=250 + 90; fire rate=3 on the 250 and 5 on the 90.
Big Cannon:
Tier 0; damage/hit=450 + 100; fire rate=1 on the 450 and 3 on the 100.

The double effects is for balancing. If the effects would be placed in a graph, you would see a M figure instead of a ^ figure.

Let's look at a fight against a Tier 0 monster with armor 0. Then each weapon does a max of:
Gatling Gun:1500
Quad Canon:960
Light Laser:2280 (Best)
Heavy Laser:1170
Rockets:1200
Big Cannon:750 (Worst)

The first noticable change is when the monster has 60 armor: Gattling Gun is now the best. That means having the Light Laser is starting to be bad news.
At 80 armor, the Light Laser is now the worst.
At 90 armor, the Heavy Laser is the best.
At 100 armor, the Light Laser has no effect any more. 5 weapons remain.
At 110 armor, the Quad Cannon is the best.
At 120 armor, the Gattling Gun is the worst.
At 150 armor, the Gattling Gun has no effect any more. 4 weapons remain.
At 170; the Big Cannon now shared the best with the Quad Cannon, after this the Big Cannon takes over.
Heavy Laser ends at armor 200.
Quad Cannon ends at armor 240.
Rockets ends at armor 250.
Armor 450 for a monster means that all weapons are obsolete. Unless trained. If the Big Cannon has tier 5, then the Armor of 900 means the end for the game.

Being the best weapon at number of armors:
Light Laser 0 to 50
Gattling Gun 60 to 80
Heavy Laser 90 to 100
Quad Cannon 110 to 170
Big Cannon 170 to 440

The Rockets never will be the best, but are a good all round weapon, and they have effect till 240 armor. I suggest having 1 monster with armor 240.

I also took a look at the tier. Due to the 20% increase, some weapons upgrade differently as well. Some are actually better after the upgrade then others. I guess this is imbalance on my part. But perhaps it could serve as an unwanted technology at the start, yet needed in the end. So some strategy can be implemented as well.

I have the excel spreadsheet with these weapon effects on armor if you want. You can simply add more or change existing ones. Although if you give your own list of weapon names and order them from heat to kinetic. I could do the calculations for you. But only if you like the idea.

Another way to come up with values is to determine what the average stat will be. Thus you take a robot with movement, attack, defense, Hp, etc. Then you assign each one an average stat. So avg Move is 4, attack 3, defense 4, Hp 10, etc. Then when you want to change stats to make things more unique, you start to change the stats. By giving yourself a baseline from which to work, you can then say, well I want this guy to have bad defense but fast. You can then give him 2 defense (bad) and 6+ move (good). Or if you just wanted poor defense and good attack, you could change it to 3 defense (poor) and 4 attack (good). I found that this really helped me figure out the starting values of my units in my tactical war game.

These values though are just starting points and balancing may be done at the player's discretion.