Back of neck tightened up after lifting weights. Can I go back to that weight?

Likely. Sounds like muscle spasms and without other symptoms. Most spasms can be treated effectively with some rest (initially), medication (anti-inflammatories such as ibuprofen, pain medications, and/or muscle relaxants), heat/ice and appropriate amounts of low impact exercise/stretching/physical therapy. After improving you should be able to return to same weight, unless it does it again.