welding resistence in spot welding
If you have a power supply with constant current mode that will work down to a short (most linear ones will, the 50A switching ones I have kick out at about 1-2V so would be more problematic) simply pass that current through the part and measure the resulting voltage drop with a multimeter. 

Suppose you have 5A available, most inexpensive meters can resolve 100uV, so you can 'see' 20u ohm resolution, not bad! Using just the ohms function, a resolution of 0.1 ohm would be more typical, with lead and contact resistance adding more errors. 

You want to use 4 wires to do this, the 'outer' ones supply the 'force' current and the inner ones to the meter sense the voltage. If done properly, only the outer ones carry any significant current and contact resistance hardly matters. This called a Kelvin connection and is the best way to measure extremely low resistances.

One minor tweak in your situation is to swap the 5A polarity and measure the voltage both ways since the different metals at each contact may cause a bit of thermocouple voltage.

Of course this is for the part without the welder connected. If you want to measure the welding current get a current sensor such as those made be LEM and connect the welding lead through it (also apply suitable power). You can probably set your scope to display resistance directly during the weld pulse if it can show V/I using two channels.