Fabricators often use SAW for the welding of large plate girders.
A one sided fillet weld would not be recommended, unless designed for the eccentricity.
In D1.1, the welding of a built up member is a design consideration. "sufficient welding shall be provided to make the parts act in unison but not less than that which is required to transmit the calculated stress between the parts joined"
For such a thin web, they could use double fillets or A B-L1a from one side with backing. I don't know why they wouldn't use a double fillet for such a small section. They could use intermittent welds, alternating sides, to reduce the amount of welding required.
A single fillet weld cannot be used in a prying condition. For example, if the flange is loaded at the toe. The weld would be in tension or prying. If the weld is designed for shear only, it can consider the eccentricity.
