I don't see how the slight weight increase should matter. The fact that your extended leg is the one with the issue(I am assuming you get this in both legs depending on what leg is at 6 o clock) suggests that you might still have the seat way too high. You might not notice when pedaling because you rapidly alternate sides and your back might be compensating subconsciously.
What happens if you coast with the weight on the seat and the cranks in 9 and 3 positions so that no leg is fully extended? If this is unproblematic then it suggests that your seat post is in fact too high.
Your knee should have quite a bend at the bottom of the pedal stroke so the knee is never fully extended. Some target an angle of approximately 140 degrees. A quick check: sit on the bike (support yourself against a wall/friend), and put one pedal in the bottom/most extended position. Your corresponding heel should be able to rest on that pedal comfortably. If you have to strech/bend your back to reach the pedal, the seat post is probably too high.
I suggest doing the coasting at 9+3 and/or do the heel-test. If one/both suggest the seat post is to high, lower it so that you pass the heel-test and go even 2-3 cm lower. You can increase it later incrementally as needed.
If this doesn't resolve the issue, then one could speculate on other reasons.
EDIT: (you could try to stand on one leg with a slightly bent knee (off the bike) and see if you experience the same issue ("immediate" burning thigh and trembling) just to check if it is an overall fitness issue that others have suggested as a possible cause. If so, put less weight on one leg when coasting and build up your strength over time. EDIT2: Consider seeing a health care professional if your issues are not resolved, progressing or seem suspicious to you)