Hey Adrian, sounds like you've pinched a nerve or done some damage to the nerves in your lower back - often leg pain, like you've described, is referred pain from the lumbar region. Particularly if the 'lactic acid' feeling was instant - this is often an indication of a pinched or bruised nerve, through poor form.
In tandem with the 'weakness' you experienced in the legs afterwards, I would bet that this is the case.
Whilst it didn't feel like the squats were any work for you, perhaps the form was not as it should have been and your lower back bore the brunt of the weight baring? This would explain the 'lactic acid' feel (pinched nerve) and the dull aching in the legs afterwards, especially if you continued on with the squat form for several repetitions?
It's hard to know without actually seeing you or feeling through the ligaments and muscle. But I would recommend, if you have a wife/gf - ask them to gently massage your lower back (including the top of your bottom, which is where this nerve has likely been pinched) and after the entire area is warmed up, ask them to knead deeper accross the entire area, working each section for you thoroughly, including down to the sides of your glutes and upper thighs.
A squat perfectly performed should see the weight of your body born on the area's of your thighs and buttocks predominantly, core tight, back solid.
Sometimes, when our core is not tight and the back is not solid, the weight is unevenly distributed and the wrong area's, whether it's the knees or the back (which are the two most common trouble spots) bare the body weights force during this exercise.
I hope that helps a little? But it sounds like referred pain to me. Get the lower lumbar region (from lattissimus dorsi, down to the top of your glutes) thoroughly worked with some remedial therapy, that should help. Any weakness you felt should be temporary and easily remedied with some tlc.
Watch your squat form! lol
Hope you get better soon