"Height" was, in all likelihood, not the correct word to have used in your letter - particularly as it relates to a relationship.
Its definition is quite clear:
height - noun
1 the measurement from base to top or (of a standing person) from head to foot :
• elevation above ground or a recognized level (typically sea level)
• the quality of being tall or high : his height seems to work to his advantage.
2 a high place or area
3 the most intense part or period of something : Ex: the height of the tourist season | at the height of his career.
When speaking in the positive, relationships (whether personal, commercial or diplomatic) usually increase, improve, become deeper, mature or solidify, etc. They do not get higher.
However, if you apply the sense of definition N°3 to your sentence, you could say something like "I hope our relationship will reach new heights of success in the year to come.