You can see how many resources you need for a Level Upgrade here:
The numbers in green show the Mech or Weapon's parameters after its Level has been upgraded.
If you don't have enough resources for the upgrade, you will see a popup showing how many A-Coins you'll need to get them.
Note: Damage increases with every Weapon upgrade and HP increases with every Mech upgrade. Some other stats (like Power, Shield Durability, Ability Damage, etc) might increase too but most of the other stats remain the same.
You can upgrade the Rank of your Mechs and Weapons every 7 Levels.
You can check how many A-Coins you need for a Rank Upgrade here:
The numbers in gold show the Mech or Weapon's parameters after its Rank has been upgraded.
You can also get a Rank Upgrade Bonus, which you can see here:
Note: When you reach the Maximum Rank for Mechs and some Weapons, you can increase their Squad Equip Limit, letting you bring more of them at once in your Squad.