First thing - if "Internet sharing" is on and you are connected to power your Macbook won't sleep, though it does turn the display off.
To start can we make sure that the computer will actually sleep.
Select "Sleep" in the Apple menu. Now wake the computer. Note the time. Do the same thing again ten minutes later but this time sleep the computer, close the lid, wait a couple of minutes then open it. Note the time again. Does this wake the computer?
I like to open Console rather than use the syslog so run Console and select "All Messages" under "System Log Queries". Now we can search in the log easily for both "wake" and "sleep".
When looking at the results for "wake" you should see some kernel messages that tell you either it waked due to a lid open "EC.LidOpen" or you touched the keyboard which will log a kernel message "The USB device Apple Internal Keyboard / Trackpad (Port 2 of Hub at 0xfa100000) may have caused a wake by issuing a remote wakeup (3)"
When looking for "sleep" the most interesting lines are those that log the AirPort power change as they mark actual system sleeps. If you have "Power Nap" turned on the you will also see kernel messages logged by RTC for "Maintenance" and "SleepService" which tells you that at time the computer was asleep but partially woke up for RTC to do it's thing.
For sleep though the best to look for is a message from WindowServer "handle_will_sleep_auth_and_shield_windows: Deferring" which it logs at sleep time.
What does 'pmset -g assertions' give you? Are there any lines set to '1'?
Given all that what do you learn about how your computer is sleeping and waking?
If it doesn't wake on a lid open perhaps you have a hardware problem?