Weapons improve, but not their base stats.
Base stats are always the same (dmg, reload, mag, etc.) for each weapon type--an EGO 120 VBI TACC Assault Rifle has the same base stats as an EGO 2,500 VBI TACC Assault Rifle.
However, the level improvements come in the form of included modifiers/bonuses. You sometimes see these as "x0.90 Reload" or "x1.05 Critical DMG." As you increase your EGO level, these bonuses become more common, more numerous, and slightly more powerful. You'll also see newer ones.
For instance, at EGO 120, you might only see a purple VBI rifle that has "x0.95 Reload," but at EGO 1,500, a purple VBI rifle might have "x0.85 Reload, x1.15 Critcal DMG, and 15% Grenade Recharge on Kill." I'm EGO 1,600 and I've seen as many as 3 bonuses so far (not counting the one randomly awarded when you fully level that weapon, or Synergy bonuses).
It's just a lengthy and slow progress, so you won't really know the differences until much much later, and those differences aren't phenomenal. But in the end, having a x1.25 Critical DMG bonus is much better than the starting x1.05 bonus.