Aerobic Septic Systems are a relatively new technology compared to the very old Anerobic systems.
The new Aerobic systems I'm familiar with a what are called "active" systems [use a blower to blow/bubble air up through the sewage in the tank to allow the air breathing bacteria to "eat" the sewage sludge. A good point about these systems is that the Aerobic bacteria do not generate as much of the foul, stinking odor that the old Anerobic systems do.
So the foul odor suggests that your active, Anerobic system may not be working properly, thus becoming "Anerobic" and thus generating the foul odors. That however is not ALL of your problems as there is another.
ALL Plumbing codes for ALL sewage systems, whether city sewer, Anerobic, and Aerobic system PLUMBING inside of structures are SUPPOSED to be SEALED so that any gasses or vapors are kept within the plumbing piping and NOT get into the structure. Vents to above the roof are required to assure that there is no pressure buildup within the household piping.
To accomplish that, structural plumbing piping codes REQUIRE that all drains have "P-traps" beneath all drains [sinks, lavatories, bath tubs, shower stalls, and the toilet P-traps are built inside of the toilets]. These traps are supposed to retain the tank drainfield
last little bit of water that drains through them, and thus "plug" the house plumbing drains so sewer gasses cannot rise up through the drains into the house.
From your description of the symptoms, I SUSPECT that you either have some kind of opening [unsealed pipe] in your plumbing [in the area of the detected odor], OR a P-trap which has "GONE DRY."
IF a sink or lavatory, or toilet is not used for such a long time that the water in its P-trap is allowed to evaporate and dry out, then the water "plug" disappears, and sewer gasses can pass through and up out of the drain. This happens often with FLOOR DRAINS [such as in basements, garages, laundry rooms, etc.] where they don't often get water flow into them.
I suggest you search for relatively "unused" drains, or cracked or broken, or unsealed plumbing pipe joints. This will probably be the source of the escaping odors.
The reason it occurs on the weekends is that y'all are there and use water more on those two days than during the week, and the system "fills up," but has time to "catch up" during the week.
That brings to mind another possible cause ----- the drainfield for the septic system MAY be undersizd for the size of your family and amount of use on the weekends, and the system backs up over the weekends until it can recover during the less used weekdays. It's also possible that the perforated pipe in the drainfield has become blocked up by tree roots, or from improper design or installation. Good luck. https://answers.yahoo.com/question/index?qid=20091222180330AAhtbWghttp://www.angieslist.com/plumbing/septic-systems.htm