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How much weight does one's college record have once one starts law school? Do employers (law firms, judges, government/PI) ask for college transcripts?

It is hard to say one way or the other with the limited information you have provided. The answer is going to be dependent upon practice area, geographic location, and the law school you graduate from. The answer also has the possibility to be employer specific as well.

Few firms do. I believe the majority of Federal Judges ask for them.

I know cravath asked for ug transcripts. A few others did as well. Mainly a formality. I know people who didnt bring it and got callbacks and offers. Still it may come up.