Yes, the progression system is designed to promote the use of multiple weapons on any character. If you are at the cap with one weapon, take up a second or multiple weapon skills. You can craft level 1 weapons or you can find them at a starter weapon vendor on the Achmedius Trade Station, standing in the corner near the other vendors.

Space and ground skill gain and experience are completely separate. You do not gain crew member experience towards the next level from space combat.

To level up a crew member, you need:
1) A full bar of "EXPERIENCE" for that crew member as displayed by the larger "yellow" progress bar for "Next Level" displayed the equipment and character information screens.
2) 5 "SKILL POINTS" gained by leveling combat and various other skills represented by the orange bars at the bottom of the "Next Level" progress bar on the equipment and character information screens.

All skills are currently capped at level 100. That will change when I raise the level cap and allow skill perks to "tier" up.

The current level cap is level 60.

SKILL POINTS: Once you reach the cap of 5 skill points, regardless of how they are earned, you will not gain additional skill points until you level up. You may gain additional secondary skill levels ups, however, no skill points are rewarded if you are at the cap of 5.

GROUND COMBAT:
Ground combat generates character "EXPERIENCE"
Ground combat generates one "SKILL POINT" for each skill level up.
Ground combat skill points are not rewarded if you are at the 5 point skill cap.
Ground combat weapon skills will not progress until you level if you are at the 5 point skill cap.
You will continue to gain general experience until you level if you are at the 5 point skill cap.

HACKING AND FIRST AID:
Hacking and first aid do not generate character "EXPERIENCE".
Hacking and first aid generate one "SKILL POINT" for each skill level up.
Hacking and first aid will not progress until you level if you are at the 5 point skill cap.

SPACE COMBAT:
Space combat does not generate character "EXPERIENCE".
Space combat does not generate skill points.
Space combat continues to generate skill experience if you are at the 5 point skill cap.

MINING:
Mining does not generate character "EXPERIENCE".
Mining does not generate skill points.
Mining progresses regardless of the skill point cap.

SALVAGING, REPAIR AND CRAFTING:
Salvaging and crafting do not generate character "EXPERIENCE".
Salvaging and crafting generate one "SKILL POINT" for each skill level up.
Salvaging and crafting progress regardless of the skill point cap. No skill points are rewarded if you are at the 5 point skill cap.