Does holding a pistol make you run further (or faster) than your primary weapon?
I wasn't able to find an 'official answer' but there were a number of sources that said only the primary affects your speed.
From this site
On movement speed (player speed is determined by the weapon in his primary slot): SMGs and Sniper Rifles have a Speed of 100% Assault Rifles have a Speed of 95% Machineguns have a Speed of 87.5% Riot Shield has a Speed of 80% A player can pick up another weapon and keep the movement speed of the weapon he spawned with.
From game FAQs
Only primaries affect running speed so pistols don't count. Also, it goes like this: SMG's/Snipers > AR's > LMG's > Riot shield
On a semi related note: Lightweight will multiply the player's movement speed by 1.1x ( 8% to 10% increase depending on the weapon).