How can "burden" in Acts 15:28–29 and Matthew 11:28 be reconciled? Acts 15:28–29 (NIV):


  It seemed good to the Holy Spirit and to us not to burden you with
  anything beyond the following requirements: You are to abstain from
  food sacrificed to idols, from blood, from the meat of strangled
  animals and from sexual immorality.


Matthew 11:28:


  "Come to me, all you who are weary and burdened, and I will give you
  rest".


The word 'burden' in Acts witnessed by Holy Spirit and used by Jesus in Matthew seems to mean the same thing, though I haven't done a Greek word study yet.

Wouldn't the combination of these scriptures give license to sin (in human meaning) if it is not violating human rights and legal demands?
Well, actually in Greek Bible these words are different. 

In Acts 15:28-29:


  ἔδοξεν γὰρ τω̨̃ πνεύματι τω̨̃ ἁγίω̨ καὶ ἡμι̃ν μηδὲν πλέον
  ἐπιτίθεσθαι ὑμι̃ν βάρος πλὴν τούτων τω̃ν ἐπάναγκες


i.e. word βάρος, that could mean also "weight"

and in Matthew 11:28:


  δευ̃τε πρός με πάντες οἱ κοπιω̃ντες καὶ πεφορτισμένοι κἀγὼ
  ἀναπαύσω ὑμα̃ς


where word πεφορτισμένοι could be translated as to be "overburden".

So the meaning of word "burdened" in your variant of translation is actually different.
If In Acts 15:28 it means some kind of obedience, while in Matthew 11:28 it means a state of man, when he is overburden, too loaded, when he is in troubles, sins and sorrow.