Have not tested that. Next time I use one, I will load some mct for a test. I am sure there are variables such as how much has already been filtered.
That is 3lbs on a 10ml syringe. 5lbs was unstable due to small plunger shaft. Any amount of unbalance would bend the shaft, break it, or fall over.
You could put 3 guide rods extending up to guide weight.
A better design would be a pvc pipe attached to wood, upright, with a rod through it, threaded on both ends, extending out top and bottom.
Thread a flange on the top to hold weight plates, and cap on bottom of rod to make contact with syringe plunger shaft.
This would give pinpoint pressure, and no need to worry about balancing a weight.
3lbs was giving 3 or 4 drops per second. It would slow down a bit because rubber plunger does begin to stick(would most likely not happen with 5lbs).
When I was done, to get the rest of the oil out, I unscrewed syringe filter a little to allow me to remove plunger (otherwise you cant remove plunger because of the fact the oil in filter will create suction because air is not allowed to flow through, and you would pull oil from syringe filter, which is opposite of what we want) Once plunger removed, rescrew the syringe filter on. Now put plunger back on, this will make nothing but air in syringe. When pressure is applied, the remaining oil is expelled. There may be some drops for the oil gods left in filter.
I don't see any reason to go over 5lbs with a 10ml syringe, but you could probably do 10 with a more directed force as mentioned in PVC and Rod design.
I have the pvc pipe and rod, I may just quick put together a prototype.
One could use plastic block for making more precise holes to fit syringes in. Easily sanitized. With upright backing to hold rod and guide. A portable collapsible one if you wanted. Use wingnuts for attaching rod and guide.
A material such as Ultra High Molecular Weight (UHMW ) Polyethylene for building.