For standard items e.g.non-named I don't think there is any weighting to drops. You do tend to find though that there are times when certain items have a higher drop rate such as when opening 10 Survial caches ther will be a lot of pistols/shotguns/holsters etc. If this happens just wait 30 mins before opening any more.
I also appear to get more MMR drops when using one so you could try using one that is available from a vendor to start with e.g. Historian.