Intermittent issues such as you describe at that throttle plate position indicates , as Pin Head so correctly pointed out - idle jet issues with fuel flow . Here's the thing about Webers that folks don't understand and more insight to what Pin Head is talking about -
You can dial in almost every bit of the fuel/air curve in any Weber carb . This is accomplished through idle jets , main jets and air jets as well as the emulsion tubes . Mains/airs take care of the available fuel to those circuits . The emulsion tubes determine how that available air/fuel is delivered . Your 38DGAS probably has F55 tubes which is an all-around and pretty evenly distributed fuel curve that easily follows main air fuel jet sizing . There are a ton of different profile emulsion tubes , an F6 - for example , will deliver a fairly even air/fuel rate at mid and higher flows but be very aggressive at low end of the mains . Same goes with the idle jets - these judge the amount of fuel/air mix available for the transition circuit holes just above the throttle plates . These are the transition circuits and progress in size and placement as the air changes position and flow speed as the throttle plates are opened . Designs vary - Holley and Carter-based designs (licensed by Weber) use a slotted transition instead of holes .
To dial a Weber into an engine , and they all must be dialed in , you set the lean best idle per instructions as well as base idle speed at fully warmed engine temps . As the engine is loaded , if it stumbles just off-idle (right when you step on the gas) this means the transition circuit is leaning out too far . Either the carb needs a larger idle jet size or the circuit has dirt in it . In your case , since this is an intermittent problem - yours has dirt in the circuit . The holes above the throttle plate as well as the idle jets are quite small - so any dirt goes there first and plugs things up . Yours is still driveable since it runs on both barrels all the time , unlike a progressive 32/36DGV series . So , that tells me one side has dirt still , possibly in the jets but more likely in the circuit itself . It can build up over time and the only way to clean it properly is to remove the carb .
Once off , remove the idle jets and the top cover , carefully . There is a small 1/8" c-clip that holds the choke linkage arm to the choke plate - watch that thing as it usually hits you in the eye before disappearing into oblivion ...
With the top cover off and idle jets removed , open the throttle all the way while upside down . With a bright light you will see a set of holes just above the point where the throttle plate sits at idle position . Spray those hole hard with brake cleaner using the straw and finish by cleaning out the float bowl as well . You don't have to remove the main jets in the bowl or the air jets on the top of the main body but it can help to clear debris . Finish with compressed air - the more the better . If you screw anything up , I have some parts left here and with pics can fix it from here as well .
One note - NEVER , EVER ADJUST THE SCREW ON THE GEARS ON THE THROTTLE LINKAGE OF A 38DGAS - THEY HAVE TO BE TIMED VERY CORRECTLY !!!
I've had to reset so many of them I'm sick of it , it takes a dual dial indicator to get them right or that carb will not respond off-idle as it should . A 38DGAS should be really crisp and quickly respond to throttle input if it's right .
Ok , fingers hurt ...
Sarge