This story is meant to be humorous. The clearest sign of that is in this verse, but the "striking" humor of it is purposely edited out in translation. The last verb doesn't mean "weary me" at all. It is one of the clearest punchlines in the Gospels.

Yet" is from a word that means "at least" and "indeed." It emphasizes the word the before it.

The word translated as "because" means "through," in the midst of," or "by (a cause)." Here, the sense is "by".

The "this" is a pronoun that can mean "this" or "that," the nearer or the further depending on usage. It appears much later in the sentence, after "widow".

"Widow" is an adjective that means "widowed" or more generally, "bereaved".  Christ uses it as a noun.  The noun is in the accusative form, not that of a subject, and it appears at the end of the phrase. This is a special Greek construction called the accusative and infinitive where the accusative infinitive takes an accusative subject.

Before the verb translated as "troubleth" an article appears making the verb act like a noun. The active gives it its accusative form.

The "troubleth" is from two Greek words, a verb and a noun, both of them uncommon for Christ. The verb means "to hand over", "to supply", and "to cause" and a lot of specific terms. It is an infinitive, uses as a noun describing the action of the verb. Since it is introduced by an article, the sense is "this supplying" or "this causing". The noun means "beating", "work", and "suffering" plus a lot of specialized meanings. The meaning comes out as to "hand out a beating" or "supply suffering."  In English, we would say "this gives me a beating". The feeling is humorous.

"I will avenge" is a Greek verb that means to "avenge", "punish", "decide" (a case), and "vindicate". Jesus uses it only in this story. It is the future tense.

The word translated as "her" is the Greek word commonly translated as third-person pronouns in English.  

"Lest" is from two Greek words, a conjunction and a negative. The conjunction means "in order that."  The negative used here is the Greek negative of a subjective opinion, commands, and requests. The sense is that "you don't want" to do something, not that it isn't done or don't think something that might be true. When the two are used together, the sense is "lest".

The word translated as "by" means "into" a place, "towards" as a direction, "in regards to" a subject, and "up to" limits in time and measure. It means "for" when referring to a purpose.

There is no "her" or "she" in this phrase, but it is implied by the feminine form of "coming".

The word translated as "continual" means "purpose", "outcome", "something done," or "goal." With the "by", the sense is "on purpose".

The word translated as "coming" primarily means "to start out". It indicates movement, especially its beginning, without indicating a direction toward or away from anything, so it works either as "come" or "go," but it is more like our phrase "being underway." Our English word "show up" captures both the "start" and "come" ideas.  It is in the form of a feminine adjective, "her showing up",

"She weary" is a verb that specifically means to "strike under the eye", "give a black eye",  "bruise", and "mortify". The form is something that might happen, "might give a black eye." "Giving someone a black eye" also had the sense of embarrassing them or damaging their reputation as it does today.

"Me" is the regular first-person pronoun in Greek.