After noticing that some perkless soldiers felt faster or slower than other perkless soldiers I decided to hop into practice and see exactly how your loadout weight affected your speed, if at all. While I was there I figured I’d also try to work out about how fast the soldiers move base and what difference there was holding different weapons. To sum it up:
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Your total loadout weight has no effect on your movespeed whatsoever.
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As loadout weight increases the stamina cost of actions increases. At 40kg it is over double the stamina cost of a 5.5kg loadout.
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Holding a rifle, SMG, shotgun, melee weapon, or any grenade type all have the same sprint speed at roughly 4.3 m/s.
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Holding an engineer hammer or AP/AT mines gives a roughly 15% movespeed boost that (appears to me) stacks multiplicatively with other boosts. ~5 m/s without the 10% run speed perk and ~5.5 m/s with it.
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Holding heavy weapons (flamethrower, MGs) gives about a 10% penalty to movespeed. 4 m/s.
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The “10% run speed” perk affects both sprinting and non-sprinting movespeed.
Hope this helps.