The example you gave is not very realistic. As Mel said, if you can lift a weight 50 times, it is way too light for you to be effective resistance training and if you can do 15lbs 50 times, then 20lbs would be way too light for a 2-rep max lift. A more realistic comparison would be 15lbs for 10 reps and 3 sets to 20lbs for 2 reps for about 8 sets. In this case, from a pure strenght building standpoint, the low reps, higher weight with similar overall reps would theoretically be better.
However, there is also the question about whether you should be lifting from purely a strength standpoint. You say, you are "extremely weak" and seem to want to focus on strength. However, someone who views themselves as extremely weak is usually just starting out. If this is the case with you, you probably cannot do a real 2-max set with proper form. Proper form is best learned using a more manageable weight. Going too heavy too soon will lead to injury and even if you don't get hurt, using improper form even when lifting heavy can be counterproductive because you may not be hitting the muscles that you are targeting due to bad form. This will lead to poor results which will kill your motivation.
If you are just starting out, train for overall strength, muscle building, and some endurance. This is a long way of agreeing with Mel's recommendation of lifting as much as you can with proper form in the 10-12 rep range. As far as what is too many reps, this also depends on the muscle you are targeting. Some respond better to high reps while others respond better to lower reps. I Train mostly in the 8-10 rep range but will go 10-12 on some exercises and on calves and abs, I often do 20 reps. So, it's hard to put a number on what is too many. For most exercises, I would say that anything more than 15 is too many unless you are specifically training a muscle for endurance or trying to add a cardio component to your resistance training (even then I would favor reducing rest periods before adding very high reps).
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