I think that Summer's weapon might be a polearm of some kind that doubles as a sniper rifle, hence one of Ruby's inspirations for creating a sniper-scythe. Remember that most teams in RWBY are set up like a party in a roleplaying game. That is, they usually consist of a Tank, a Mage, a Rogue (close-distance attacker), & a Ranger (long-distance attacker). I see Summer as the Ranger of Team STRQ with a weapon that has a long reach & can be used mostly for long-distance attacks. My guess is a spear or a staff, but I'm mostly leaning towards a spear.