I understand how they came up with the 483 years in Daniel 9, but how do we know from scripture that the 69 weeks is supposed to mean 69 weeks of seven years? Why do they do this or are they just figuring this backward and then saying well it must have meant years and not weeks?
One year for one day is a common substitution in prophecy:
"For forty years -- one year for each of the forty days you explored the land -- you will suffer for your sins and know what it is like to have me against you'" (Numbers 14:34).
"And when you have completed them, lie again on your right side; then you shall bear the iniquity of the house of Judah forty days. I have laid on you a day for each year" (Ezekiel 4:6).
In addition, God issued commands for sabbatical years, which He treated as sets of seven years or "weeks." "And you shall count seven sabbaths of years for yourself, seven times seven years; and the time of the seven sabbaths of years shall be to you forty-nine years" (Leviticus 25:8).
That he did not mean a literal 70 weeks can be determined by the context. Seven weeks were assigned to the rebuilding of Jerusalem. That was an impossibly short period of time. The walls alone, though done in record time took 52 days by themselves (Nehemiah 6:15); thus, we know that the time given in this prophecy represents another scale. Since God used the scale of 1 day equals 1 year in the past, it was a reasonable substitution and one that fits all events.
Interestingly, in the Hebrew, it literally says that God appointed seventy sevens. The time scale isn't actually mentioned, but since "sevens" is also the word for a week, it is translated as such. A bit later in Daniel 10:2, Daniel mentions a three week period, but to distinguish it from the weeks he just mentioned in Daniel 9, he called it "weeks of days" in the Hebrew. This also is a clue that the weeks in Daniel 9 were weeks of another time period.