Currently the max weight is 1000kg. However in a future update they're looking to raise this

any idea when the big update will come?

Yea, I have the same question. I Don't use all weapon slots and no kits couse I'm at the limit, and I have the feeling that my oponents in the campaign are hevier nhan me.

Yes, i have the same question! How the other players have Last Armour and 6 weapons on their head and i use only 2 swords,1 shotgun and a damn low lvl armour for Low weight? Is it possible to upgrade the weight, or is a damn hack?!

I am angry about this, serious...

At all depends what you equip on to your mech. Take a look at the item weights carefully and see if there are any equivalent items with a lower weight. Just a couple examples:

Swords are HEAVY!!! If you equip a sword, you ideally want to fight in the lower ranges so don't even bother with top weapons.

Bullet modules are heavy! On top of this, any strong bullet weapon is also heavy. If you're going to equip bullet weapons, only aim for 2 and understand you won't get much more on to your mech if you choose to do this.

Duo heat/energy modules are HEAVYYYYY!!!!! Instead try to equip the modules that only effect regen and cool down. These are so much more worth it. If not, use the modules that only effect energy or heat (you can use multiple, just don't use the duo one). This will help reduce your weight.

Decide what damage your mech does. If you do heat damage, then teleport and charge aren't going to favour you. Choose the lowest level possible for these, so you still have the option to close a gap however reduce the weight for these items as the damage from using these isn't going to be helpful even at higher levels.
For energy, only teleport and hook will help, so low level charge.
For physical charge is the only useful one. There is a low level physical hook so pick that up and choose a low level teleport.

Beat heat mechs no problem? Then get rid of your multi-resistant module. Instead equip a physical and energy resistant module. While it takes up two slots, it's light and if you're beating heat mechs easily that resistance is going to waste (same goes if you're finding other mechs easy to beat).

These are some simple tips that should help when it comes to weight.