Politics of religion
Nonetheless, we can pull out the basic sense. At the beginning, he talks about 'censure' against his 'voluntary exile' (ie, his trip to New England), and protests that his 'practize' was 'regular'. This probably means that in carrying out his ecclesiastical duties in Yarmouth, contrary to what some had said about him, he had obeyed orthodox religious doctrine.
'... Burdett left Yarmouth and travelled to New England because he was being prosecuted.'
He then says that the grounds of his 'secession' - that is, the reason why he left - was 'impetuous and malicious prosecution, importable expense'. This would seem to indicate legal proceedings and their attendant costs - also that he left Yarmouth because of court cases against him. Finally, he indicates that he is keen to return to England when he can, and that he wishes to remain in Archbishop Laud's favour.
It would appear that we now have an answer to our original question. George Burdett left Yarmouth and travelled to New England because he was being prosecuted. And we can check on this. Consulting another finding aid, the Calendar of State Papers, Domestic, we find a case against 'George Burdett of Yarmouth' brought to the court of High Commission in February 1635, by Matthew Brooks and others, concerning the religious content of Burdett's preaching.
It seems he was found guilty, removed from his office, ordered to be further examined on his religious orthodoxy, and to pay the legal costs of the case. Burdett left Yarmouth to escape these costs (later references show that they remained unpaid) and obviously had lost any position of power he held there.
Having arrived in New England and become enmeshed once again in political and religious struggle, he seems to have taken the opportunity to ingratiate himself once more with the English Church hierarchy, writing to the archbishop as an informer on the colonies.