Collinear follows the model of collaborate, collide, &c.: the m of the Latin prefix com- ("together") is assimilated to the initial l of the Latinate stem (cf. commiserate, contemporary, coæval, corrode). It's pronounced with the stress on the second syllable, & therefore an indeterminate vowel or at most a short o.
An excuse for colinear might be that you're treating linear as a native word, following the model of copilot, co-worker, &c.—cases in which the prefix is reduced to co- irrespective of the initial letter of the stem.† I imagine people who write it thus also pronounce it with at least a secondary stress on the first syllable, & with a long o.
Pace @Carl I don't think a general predilection among the British for writing double l has much to do with it, though a preference for more traditional word-forms might. Counts of occurrences in published works from Google Ngrams suggest that colinear & its derivatives are disfavoured only slightly less in U.S. than in British English (an odds ratio of 1.4 over 1999 – 2008).
#define word list & corpora
words <- "collinear, colinear, collinearity, colinearity, multicollinear, multicolinear, multicollinearity, multicolinearity"
corpora <- c("eng_gb_2012", "eng_us_2012")
# fetch word counts
dd <- ngram(words, corpora, year_start = 1999, smoothing = 0, count = T, tag = NULL, case_ins = TRUE)
# reduce derivatives
dd$stem <- factor(gsub("multi|ity", "", tolower(dd$Phrase)))
xtabs(Count~stem+Corpus, data=dd) -> tb
What may well be muddying the waters, however, is that there are more recent coinings of the word with different senses from the geometric one "together in a line" (first known use in 1863 according to my dictionary); in these we'd naturally expect the form colinear just because people don't make up Latin words any more. Wikipedia has an article on colinear maps & the on-line Merriam-Webster dictionary gives a second sense of colinear (but not collinear), "having corresponding parts arranged in the same linear order", that finds its use in Genetics & Molecular Biology.
† If you really want to write colinear & anyone's picking on you because of it, ask them if they write complanar.