Not putting on weight please help.

Ok well I started working out 4 weeks ago from today and still have not put on any extra weight. I can see the results but still I never really had any fat to to burn so i dont know what's going on. Im 16, 6'1, and only 140 pounds. Here is my workout, please do your best in critiquing my workout so I'll get better results.
Schedule: (keep in mind I usually do 3 sets of 20 per exercise, unless I say otherwise.)

Sunday: Back/Bicep/Forearms (equipment: 2, 20 pound dumbells)
Back- Bent-Over two-dumbell row,  Bent over two-dumbell row palms in.
Bicep- Alternate Hammer curls, Concentration curls
Forearm- Palms-up wrist curl, Seated one-arm dumbell palms down wrist curl (use 6 pound dumbell)

Monday:
Off day/ Cardio

Tuesday: Shoulders/Traps (equipment: 2, 20 pound dumbells)
Traps- Dumbbell Shrugs, Dumbbell Incline Shoulder Raise, Standing Dumbell Upright Row.
Shoulders- Arm circles (usually 30 per set), Arnold Dumbell Press

Wednesday:
Off day/Cardio

Thursday: Chest/Triceps
Chest- Around the Worlds (10 per set), Bent-Arm Dumbbell Pullover, Dumbbell Bench Press
Triceps- Across Face Dumbbell Tricep Extension, Dumbbell one arm tricep extension (10 per set, 6 pound dumbbell)

Friday: Legs/Calves
Varius activities, not very focused on my legs so I'll usually just jog.

Saturday:
Off day/Cardio

Also everynight I work out my abs:
3 sets of 2 airbikes
3 sets of 20 heel touchers
3 sets of 20 bent knee hip raise

Your probably not eating enough. And a full body routine would be much better then bodypart splits at your experience level. Bodypart splits are for more advanced lifters who arent able to work up the necessary volume to grow in a full body.

Your probably not eating enough.

"No citizen has a right to be an amateur in the matter of physical
training...what a disgrace it is for a man to grow old without ever seeing the
beauty and strength of which his body is capable."

It sounds like your working out at home, due to the equipment you say you have but correct me if im wrong. If this is the case you cannot expect to be making gains if you are using the same weights every time. Also the exercises you are doing do not look very good, if you are serious about getting bigger and stronger you should either go to a real gym or buy more equipment. And you should be focused on your legs because they are very important and if you neglect them you will be very sorry in the future. You should try to do important compound exercises instead of what you are doing like: Squat, Bench Press, Deadlift, Overhead Press, Power Clean. Also with what you are doing, if you have no other option, honestly i think doing body weight exercises would be more effective than your routine.

Also remember to gain weight, make sure you eat over 9000 calories!

Start squatting
If you really want to gain weight fast, stop the cardio, otherwise do it once a week only. But really, start squating. You also need deadlifts!!

You should focus on these, they are extremely important:
Squats
Deadlifts
Overhead Presses (either barbell or dumbbell)
Bench press
Power Cleans
Barbell rows (do them until you learn proper power cleans)
Pull ups :)

Thanks so far everyone, and yes I am working at home, I'll try and get some membership soon, and thanks for the advice about compounds I'll start doing more of them instead of isolated exercises.

ravenpt and smoundz gave great advice.

focus more on your diet though.  your body is fighting against you right now.  you're young, and you're literally going to have to eat every 3 hours and force it down until you want to vomit probably... in order to gain weight.  your caloric needs per day are very high i'm sure. 

focus on EAT EAT EAT EAT EAT!

training is also necessary, but it plays a much smaller portion of the equation

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